| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 25.1-a6 |
25.1-a |
$8$ |
$30$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$4.48185$ |
$(-a-1)$ |
0 |
$\Z/10\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.1.1[2] |
$1$ |
\( 2 \) |
$1$ |
$1248.063226$ |
0.744201123 |
\( -16554983445 a^{3} + 49664950335 a + 10231546590 \) |
\( \bigl[a^{3} - 2 a\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a + 1\) , \( -35 a^{3} - 31 a^{2} + 85 a + 21\) , \( 110 a^{3} + 91 a^{2} - 273 a - 59\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(-35a^{3}-31a^{2}+85a+21\right){x}+110a^{3}+91a^{2}-273a-59$ |
| 25.1-a8 |
25.1-a |
$8$ |
$30$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$4.48185$ |
$(-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.1.4[2] |
$1$ |
\( 2 \) |
$1$ |
$49.92252905$ |
0.744201123 |
\( -16554983445 a^{3} + 49664950335 a + 10231546590 \) |
\( \bigl[a^{3} - 2 a + 1\) , \( a^{3} + a^{2} - 4 a - 3\) , \( a^{2} + a - 1\) , \( -199462 a^{3} - 165053 a^{2} + 496253 a + 109138\) , \( -50977357 a^{3} - 42163431 a^{2} + 126872829 a + 27900618\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-3\right){x}^{2}+\left(-199462a^{3}-165053a^{2}+496253a+109138\right){x}-50977357a^{3}-42163431a^{2}+126872829a+27900618$ |
| 81.1-a1 |
81.1-a |
$8$ |
$30$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{12} \) |
$5.19129$ |
$(-a^3+a^2+3a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 5$ |
3B.1.2, 5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$62.01676032$ |
0.924491278 |
\( -16554983445 a^{3} + 49664950335 a + 10231546590 \) |
\( \bigl[a^{2} + a - 1\) , \( 0\) , \( a\) , \( -5 a^{3} - 23 a^{2} - 28 a - 6\) , \( 264 a^{3} + 140 a^{2} - 825 a - 176\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}+a{y}={x}^{3}+\left(-5a^{3}-23a^{2}-28a-6\right){x}+264a^{3}+140a^{2}-825a-176$ |
| 81.1-a3 |
81.1-a |
$8$ |
$30$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
81.1 |
\( 3^{4} \) |
\( 3^{12} \) |
$5.19129$ |
$(-a^3+a^2+3a-2)$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 5$ |
3B.1.1, 5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$558.1508429$ |
0.924491278 |
\( -16554983445 a^{3} + 49664950335 a + 10231546590 \) |
\( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + 3 a + 1\) , \( 1\) , \( -14 a^{3} + 42 a - 26\) , \( -32 a^{3} + 96 a - 51\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+3a+1\right){x}^{2}+\left(-14a^{3}+42a-26\right){x}-32a^{3}+96a-51$ |
| 841.10-a1 |
841.10-a |
$8$ |
$30$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
841.10 |
\( 29^{2} \) |
\( 29^{6} \) |
$6.95528$ |
$(-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$103.6460095$ |
1.545063486 |
\( -16554983445 a^{3} + 49664950335 a + 10231546590 \) |
\( \bigl[a^{2} - 1\) , \( a^{3} - 4 a\) , \( a^{3} - 3 a + 1\) , \( -4 a^{3} - 15 a^{2} + 18 a - 3\) , \( 17 a^{3} + 44 a^{2} - 78 a - 29\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(-4a^{3}-15a^{2}+18a-3\right){x}+17a^{3}+44a^{2}-78a-29$ |
| 841.10-a4 |
841.10-a |
$8$ |
$30$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
841.10 |
\( 29^{2} \) |
\( 29^{6} \) |
$6.95528$ |
$(-a^3+a^2+4a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$103.6460095$ |
1.545063486 |
\( -16554983445 a^{3} + 49664950335 a + 10231546590 \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 4 a\) , \( a^{3} - 2 a + 1\) , \( -61310 a^{3} - 51000 a^{2} + 151961 a + 33437\) , \( -8814438 a^{3} - 7286362 a^{2} + 21946253 a + 4825929\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(-61310a^{3}-51000a^{2}+151961a+33437\right){x}-8814438a^{3}-7286362a^{2}+21946253a+4825929$ |
| 841.7-a6 |
841.7-a |
$8$ |
$30$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
841.7 |
\( 29^{2} \) |
\( 29^{6} \) |
$6.95528$ |
$(-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$103.6460095$ |
1.545063486 |
\( -16554983445 a^{3} + 49664950335 a + 10231546590 \) |
\( \bigl[a\) , \( a^{3} - 4 a\) , \( a^{3} - 2 a\) , \( -1326257 a^{3} - 1096940 a^{2} + 3300819 a + 725883\) , \( -870443666 a^{3} - 719936036 a^{2} + 2166386079 a + 476409613\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(-1326257a^{3}-1096940a^{2}+3300819a+725883\right){x}-870443666a^{3}-719936036a^{2}+2166386079a+476409613$ |
| 841.7-a8 |
841.7-a |
$8$ |
$30$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
841.7 |
\( 29^{2} \) |
\( 29^{6} \) |
$6.95528$ |
$(-a^3-a^2+2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$103.6460095$ |
1.545063486 |
\( -16554983445 a^{3} + 49664950335 a + 10231546590 \) |
\( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} - a^{2} + 2 a + 2\) , \( a^{2} + a - 1\) , \( 28 a^{3} - 85 a^{2} + 44 a + 13\) , \( -229 a^{3} + 748 a^{2} - 502 a - 143\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+2a+2\right){x}^{2}+\left(28a^{3}-85a^{2}+44a+13\right){x}-229a^{3}+748a^{2}-502a-143$ |
| 841.8-a2 |
841.8-a |
$8$ |
$30$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
841.8 |
\( 29^{2} \) |
\( 29^{6} \) |
$6.95528$ |
$(2a^3+a^2-7a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$103.6460095$ |
1.545063486 |
\( -16554983445 a^{3} + 49664950335 a + 10231546590 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( a^{2} + a - 3\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -4944643 a^{3} - 4089726 a^{2} + 12306253 a + 2706273\) , \( 6260338923 a^{3} + 5177869806 a^{2} - 15580916689 a - 3426396906\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(a^{2}+a-3\right){x}^{2}+\left(-4944643a^{3}-4089726a^{2}+12306253a+2706273\right){x}+6260338923a^{3}+5177869806a^{2}-15580916689a-3426396906$ |
| 841.8-a3 |
841.8-a |
$8$ |
$30$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
841.8 |
\( 29^{2} \) |
\( 29^{6} \) |
$6.95528$ |
$(2a^3+a^2-7a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$103.6460095$ |
1.545063486 |
\( -16554983445 a^{3} + 49664950335 a + 10231546590 \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{2} + a + 2\) , \( a^{2} + a - 2\) , \( 46 a^{3} + 3 a^{2} - 179 a - 37\) , \( 315 a^{3} + 91 a^{2} - 1189 a - 251\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(46a^{3}+3a^{2}-179a-37\right){x}+315a^{3}+91a^{2}-1189a-251$ |
| 841.9-a3 |
841.9-a |
$8$ |
$30$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
841.9 |
\( 29^{2} \) |
\( 29^{6} \) |
$6.95528$ |
$(a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$103.6460095$ |
1.545063486 |
\( -16554983445 a^{3} + 49664950335 a + 10231546590 \) |
\( \bigl[a^{2} - 2\) , \( a^{3} - 3 a - 1\) , \( a^{3} - 3 a + 1\) , \( 3 a^{3} - 4 a^{2} - 24 a - 18\) , \( 9 a^{3} - 14 a^{2} - 72 a - 1\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a^{3}-3a-1\right){x}^{2}+\left(3a^{3}-4a^{2}-24a-18\right){x}+9a^{3}-14a^{2}-72a-1$ |
| 841.9-a6 |
841.9-a |
$8$ |
$30$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
841.9 |
\( 29^{2} \) |
\( 29^{6} \) |
$6.95528$ |
$(a^2-a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.4.1[2] |
$1$ |
\( 2 \) |
$1$ |
$103.6460095$ |
1.545063486 |
\( -16554983445 a^{3} + 49664950335 a + 10231546590 \) |
\( \bigl[a^{3} - 2 a\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{2} + a - 2\) , \( -79220 a^{3} - 66357 a^{2} + 195350 a + 43016\) , \( 13008496 a^{3} + 10780866 a^{2} - 32329042 a - 7110931\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(-79220a^{3}-66357a^{2}+195350a+43016\right){x}+13008496a^{3}+10780866a^{2}-32329042a-7110931$ |
| 961.10-b4 |
961.10-b |
$8$ |
$30$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
961.10 |
\( 31^{2} \) |
\( 31^{6} \) |
$7.07221$ |
$(-2a^3-2a^2+6a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.4.1[2] |
$1$ |
\( 2 \) |
$0.111217262$ |
$388.2543833$ |
2.574792903 |
\( -16554983445 a^{3} + 49664950335 a + 10231546590 \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -34 a^{3} - 41 a^{2} + 90 a + 18\) , \( 123 a^{3} + 135 a^{2} - 322 a - 72\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-34a^{3}-41a^{2}+90a+18\right){x}+123a^{3}+135a^{2}-322a-72$ |
| 961.10-b6 |
961.10-b |
$8$ |
$30$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
961.10 |
\( 31^{2} \) |
\( 31^{6} \) |
$7.07221$ |
$(-2a^3-2a^2+6a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.4.1[2] |
$1$ |
\( 2 \) |
$1.668258938$ |
$25.88362555$ |
2.574792903 |
\( -16554983445 a^{3} + 49664950335 a + 10231546590 \) |
\( \bigl[a^{3} - 2 a\) , \( a^{3} - 2 a\) , \( 1\) , \( -229681 a^{3} - 190239 a^{2} + 571047 a + 125597\) , \( -63266176 a^{3} - 52330761 a^{2} + 157450333 a + 34625138\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+{y}={x}^{3}+\left(a^{3}-2a\right){x}^{2}+\left(-229681a^{3}-190239a^{2}+571047a+125597\right){x}-63266176a^{3}-52330761a^{2}+157450333a+34625138$ |
| 961.7-b3 |
961.7-b |
$8$ |
$30$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
961.7 |
\( 31^{2} \) |
\( 31^{6} \) |
$7.07221$ |
$(a^3+2a^2-3a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.4.1[2] |
$1$ |
\( 2 \) |
$0.556086312$ |
$77.65087667$ |
2.574792903 |
\( -16554983445 a^{3} + 49664950335 a + 10231546590 \) |
\( \bigl[a^{2} - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -2 a^{3} - 17 a^{2} + 53 a - 39\) , \( 28 a^{3} - 155 a^{2} + 201 a - 55\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-1\right){x}^{2}+\left(-2a^{3}-17a^{2}+53a-39\right){x}+28a^{3}-155a^{2}+201a-55$ |
| 961.7-b6 |
961.7-b |
$8$ |
$30$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
961.7 |
\( 31^{2} \) |
\( 31^{6} \) |
$7.07221$ |
$(a^3+2a^2-3a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.4.1[2] |
$1$ |
\( 2 \) |
$0.333651787$ |
$129.4181277$ |
2.574792903 |
\( -16554983445 a^{3} + 49664950335 a + 10231546590 \) |
\( \bigl[a^{3} - 3 a + 1\) , \( -a^{2} + 3\) , \( 1\) , \( -945799 a^{3} - 782263 a^{2} + 2353930 a + 517653\) , \( 524197265 a^{3} + 433558794 a^{2} - 1304637727 a - 286902673\bigr] \) |
${y}^2+\left(a^{3}-3a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-945799a^{3}-782263a^{2}+2353930a+517653\right){x}+524197265a^{3}+433558794a^{2}-1304637727a-286902673$ |
| 961.8-b2 |
961.8-b |
$8$ |
$30$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
961.8 |
\( 31^{2} \) |
\( 31^{6} \) |
$7.07221$ |
$(-a^3+5a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.4.1[2] |
$1$ |
\( 2 \) |
$0.111217262$ |
$388.2543833$ |
2.574792903 |
\( -16554983445 a^{3} + 49664950335 a + 10231546590 \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{3} + 2 a + 1\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -70144 a^{3} - 58044 a^{2} + 174511 a + 38379\) , \( -10627479 a^{3} - 8789766 a^{2} + 26450255 a + 5816663\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+2a+1\right){x}^{2}+\left(-70144a^{3}-58044a^{2}+174511a+38379\right){x}-10627479a^{3}-8789766a^{2}+26450255a+5816663$ |
| 961.8-b7 |
961.8-b |
$8$ |
$30$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
961.8 |
\( 31^{2} \) |
\( 31^{6} \) |
$7.07221$ |
$(-a^3+5a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.4.1[2] |
$1$ |
\( 2 \) |
$1.668258938$ |
$25.88362555$ |
2.574792903 |
\( -16554983445 a^{3} + 49664950335 a + 10231546590 \) |
\( \bigl[a + 1\) , \( -a^{3} - a^{2} + 3 a + 1\) , \( a^{2} - 1\) , \( -22 a^{3} - 7 a^{2} + 86 a - 51\) , \( 10 a^{3} + 29 a^{2} + 68 a - 169\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+1\right){x}^{2}+\left(-22a^{3}-7a^{2}+86a-51\right){x}+10a^{3}+29a^{2}+68a-169$ |
| 961.9-b2 |
961.9-b |
$8$ |
$30$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
961.9 |
\( 31^{2} \) |
\( 31^{6} \) |
$7.07221$ |
$(2a^3-8a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.4.1[2] |
$1$ |
\( 2 \) |
$0.333651787$ |
$129.4181277$ |
2.574792903 |
\( -16554983445 a^{3} + 49664950335 a + 10231546590 \) |
\( \bigl[a^{2} - 2\) , \( a^{3} + a^{2} - 2 a - 2\) , \( a^{2} - 2\) , \( -3449313 a^{3} - 2852961 a^{2} + 8584610 a + 1887842\) , \( 3646894359 a^{3} + 3016313673 a^{2} - 9076497964 a - 1996011239\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-2a-2\right){x}^{2}+\left(-3449313a^{3}-2852961a^{2}+8584610a+1887842\right){x}+3646894359a^{3}+3016313673a^{2}-9076497964a-1996011239$ |
| 961.9-b3 |
961.9-b |
$8$ |
$30$ |
\(\Q(\zeta_{15})^+\) |
$4$ |
$[4, 0]$ |
961.9 |
\( 31^{2} \) |
\( 31^{6} \) |
$7.07221$ |
$(2a^3-8a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-60$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5B.4.1[2] |
$1$ |
\( 2 \) |
$0.556086312$ |
$77.65087667$ |
2.574792903 |
\( -16554983445 a^{3} + 49664950335 a + 10231546590 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{3} - 3 a + 1\) , \( 62 a^{3} + 19 a^{2} - 234 a - 62\) , \( 439 a^{3} + 129 a^{2} - 1605 a - 346\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(62a^{3}+19a^{2}-234a-62\right){x}+439a^{3}+129a^{2}-1605a-346$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
