Curves from the paper 'The functional equation for L-functions of hyperelliptic curves'

Name|Polynomials|Link to Plain Text|Link to .sobj file
Example 3.11: |g = x^5 - 3x^4 - 3x^3 - 3*x^2 - 3x - 1
h = x^2 + 3x + 1|<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c4_3_7_101_163.sage" class="download">Download uncompressed</a>|<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c4_3_7_101_163.sobj" class="download">Download compressed</a>
Example 3.12: |g = x^7 + x^6 + 2x^5 + 2x^4 + 2x^3 - 1
h = -x^3 + x^2 + x + 2|<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c4_27_121_37.sage" class="download">Download uncompressed</a>|<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c4_27_121_37.sobj" class="download">Download compressed</a>
Example 3.13: |g = x^9 - 2x^8 + x^7 - 2x^4 + 2x^3 + 2x^2 + x
h = -2x^4 + x^3 - 2x^2 - x - 1|<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c9_343_31_53.sage" class="download">Download uncompressed</a>|<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c9_343_31_53.sobj" class="download">Download compressed</a>
Example 3.14: |g = x^11 + 3x^4 + 2x^3 - 3x^2 - 2x
h = -3x^3 + x^2 + 3x + 1|<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c7_227_1227_1609.sage" class="download">Download uncompressed</a>|<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c7_227_1227_1609.sobj" class="download">Download compressed</a>
Example 3.15: |g = x^13 + x^12 + x^11 + x^10 + x^9 + x^8
- x^7 - x^6 + x^5 + x^4 + x^3
h = x^6 + x^5 - x^3 + x^2 + x + 1|<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c7_11_13_89_431_857.sage" class="download">Download uncompressed</a>|<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c7_11_13_89_431_857.sobj" class="download">Download compressed</a>
Example in 4.1: |g = x^7 - 2*x^6 - 2*x^4 + x^3 + 3x^2 + x
h = 3x^3 + 3x^2 + 2x + 1|<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c3_125_169_97.sage" class="download">Download uncompressed</a>|<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c3_125_169_97.sobj" class="download">Download compressed</a>
Example in 4.2: |g = x^9 - x^8 + x^7 + x^5 + x^3
h = -x^4 + 1|<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c65536_317.sage" class="download">Download uncompressed</a>|<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c65536_317.sobj" class="download">Download compressed</a>
Example in 4.3:|y^3 = x^4-x^2+1|<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c256_531441.sage" class="download">Download uncompressed</a>|<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c256_531441.sobj" class="download">Download compressed</a>
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Structure of the data files

0: genus, 1: g(x), 2: h(x), 3: conductor, 4: bad primes, 5:bad factors, 6: bound M, 7: root number or sign, 8: L-series up to M

suggested use:

sage: c=load('c7_227_1227_1609.sobj')
sage: c[0]
5
sage: c[2]
-3*x^3 + x^2 + 3*x + 1
 

Further examples

Name||g=||Polynomials||Remarks||Link to .sobj
c11_13_31_79_163||2||g = x^5 - 3*x^4 - 3*x^3 - 3*x^2 - 3*x - 3
h = 4*x^2 + 2*x - 1||semistable at 2, root number -1,
conductor 11 * 13 * 31 * 79 * 163||<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c11_13_31_79_163.sobj" class="download">Download compressed</a>
c256_11_31_347||4||g = x^9 - 2*x^8 - 2*x^7 + x^6 - x^5 - x^4
h = -2*x^4 - x^3 + x^2 - x - 1||not s.s. at 2, r.n. -1, L_2=(1 - T) * (8T^6+...)
cond. 2^8 * 11 * 31 * 347||<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c256_11_31_347.sobj" class="download">Download compressed</a>
c2_11_242059||4||g = x^9
h = x^4 + x^3 - x^2 - 1||s.s. at 2, r.n. -1,
cond. 2 * 11 * 242059||<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c2_11_242059.sobj" class="download">Download compressed</a>
c81_59_6047||4||g = x^9 - x^7 - x^3 - x^2
h = x^3 + 1||s.s. at 2, L_3 = (1-T^4),
cond. 3^4 * 59 * 6047||<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c81_59_6047.sobj" class="download">Download compressed</a>
c27_19_347||3||g = x^7 + x^6 - x^5 - x^4 - x^3 - x^2 + x
h = -2*x^3 - 2*x^2 + x - 1||s.s. at 2, L_3 = (1+T)(1+T^2),
cond. 3^3 * 19 * 347||<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c27_19_347.sobj" class="download">Download compressed</a>
c27_125_23||3||g = x^7 - x^5 - x^3 - x^2 - 2*x
h = -x^3 + 2*x^2 + 2*x + 1||s.s. at 2, gcd(f,f')>1, L_3=(1+T)*(3T^2+1), L_5=(1-T)(1-T^2), L_23=(1-T)*(529T^4+...), cond. 3^3 * 5^3 * 23||<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c27_125_23.sobj" class="download">Download compressed</a>
c27_125_23||3||g = x^7 - x^5 + x^2 + x
h = 2*x^3 + x^2 + 1||s.s. at 2, gcd(f,f')>1, L_3=(1+T)*1, cond. 3^7 * 5 * 17||<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c27_125_23.sobj" class="download">Download compressed</a>
c131072_11_23_67||5||g = x^11 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^2
h = -x^4 - 1||not s.s. at 2, r.n. 1, L_2=(2*T^2 - T + 1) * (2*T^2 + 2*T + 1), cond. 2^17 * 11 * 23 * 67||<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c131072_11_23_67.sobj" class="download">Download compressed</a>
c32_2381_9547||5||g = x^11 - x^9 - x^8 - x^6 + x^4 + x^3 + x
h = x^5 - x^3 - x^2 + x - 1||s.s. at 2, r.n. 1, L_2=(1-T) * (T^4 + T^3 + T^2 + T + 1), cond. 2^5 * 2381 * 9547||<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c32_2381_9547.sobj" class="download">Download compressed</a>
c3125_11_169||3||g = x^7 - 2*x^6 + x^5 - x^4 + x^3 - 2*x^2 + x
h = -2*x^3 + x^2 - 2*x||s.s. at 2, gcd(f,f')>1, r.n. -1, L_5=(1-T)*1, L_13=(1-T^2)*(13T^2+ ...),
cond. 5^5 * 11 * 13^2||<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c3125_11_169.sobj" class="download">Download compressed</a>
c32268413||4||g = x^9
h = x^4 - x^3 - x - 1||s.s. at 2, r.n. 1, bad primes p=32268413, L_p = (1+ ...) irrelevant
cond. 32268413||<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c32268413.sobj" class="download">Download compressed</a>
c8_481198723||5||g = x^11 - x^10 + x^8
h = -x^3 - 1||s.s. at 2, r.n. -1, cond. 2^3 * 481198723||<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c8_481198723.sobj" class="download">Download compressed</a>
c428854201||5||g = x^11 + x^10 + x^8 - x^7 - x^6 + x^5 - x^4
h = x^3 + x^2 - x + 1||s.s. at 2, r.n. 1, bad primes p=428854201, L_p = (1+ ...) irrelevant
cond. 428854201||<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c428854201.sobj" class="download">Download compressed</a>
c125_7_11_189_961||3||g = x^7 - 2*x^6 - 2*x^4 + x^3 - 2*x^2 + x
h = x^3 + x^2 - x||r.n. 1, bad primes 5,7,11,17,31,
L_5=(1-T)(1+T)^2*1,
cond. 5^3 * 7 * 11 * 17^2 * 31^2||<a href="https://www.uni-ulm.de/fileadmin/website_uni_ulm/mawi.inst.100/mitarbeiter/boerner/hyperell/c125_7_11_189_961.sobj" class="download">Download compressed</a>
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