| 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-a2 |
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 |
\( 16554983445 a^{3} - 49664950335 a + 26786530035 \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( a^{3} - 2 a + 1\) , \( -45 a^{3} - 39 a^{2} + 113 a + 26\) , \( -258 a^{3} - 214 a^{2} + 641 a + 138\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+2\right){x}^{2}+\left(-45a^{3}-39a^{2}+113a+26\right){x}-258a^{3}-214a^{2}+641a+138$ |
| 25.1-a4 |
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 |
\( 16554983445 a^{3} - 49664950335 a + 26786530035 \) |
\( \bigl[a^{2} - 1\) , \( a - 1\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -11484892 a^{3} - 9499051 a^{2} + 28583937 a + 6285889\) , \( 29062760688 a^{3} + 24037545339 a^{2} - 72332262037 a - 15906576101\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{3}+a^{2}-2a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-11484892a^{3}-9499051a^{2}+28583937a+6285889\right){x}+29062760688a^{3}+24037545339a^{2}-72332262037a-15906576101$ |
| 81.1-a5 |
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 |
\( 16554983445 a^{3} - 49664950335 a + 26786530035 \) |
\( \bigl[1\) , \( -1\) , \( a^{3} - 3 a + 1\) , \( -17 a^{3} + 51 a - 32\) , \( 52 a^{3} - 156 a + 82\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}-{x}^{2}+\left(-17a^{3}+51a-32\right){x}+52a^{3}-156a+82$ |
| 81.1-a8 |
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 |
\( 16554983445 a^{3} - 49664950335 a + 26786530035 \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a^{2} - 1\) , \( -2561 a^{3} - 2096 a^{2} + 6386 a + 1346\) , \( -98327 a^{3} - 81248 a^{2} + 244768 a + 53612\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-2561a^{3}-2096a^{2}+6386a+1346\right){x}-98327a^{3}-81248a^{2}+244768a+53612$ |
| 841.10-a5 |
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 |
\( 16554983445 a^{3} - 49664950335 a + 26786530035 \) |
\( \bigl[a^{3} - 2 a + 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -8 a^{3} - 16 a^{2} + 26 a - 1\) , \( -54 a^{3} - 57 a^{2} + 161 a + 39\bigr] \) |
${y}^2+\left(a^{3}-2a+1\right){x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(-8a^{3}-16a^{2}+26a-1\right){x}-54a^{3}-57a^{2}+161a+39$ |
| 841.10-a8 |
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 |
\( 16554983445 a^{3} - 49664950335 a + 26786530035 \) |
\( \bigl[1\) , \( -a^{2} - a + 3\) , \( a^{3} - 2 a + 1\) , \( -3561535 a^{3} - 2945719 a^{2} + 8864042 a + 1949293\) , \( 5022573969 a^{3} + 4154125293 a^{2} - 12500331294 a - 2748945842\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(-a^{2}-a+3\right){x}^{2}+\left(-3561535a^{3}-2945719a^{2}+8864042a+1949293\right){x}+5022573969a^{3}+4154125293a^{2}-12500331294a-2748945842$ |
| 841.7-a2 |
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 |
\( 16554983445 a^{3} - 49664950335 a + 26786530035 \) |
\( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( -a^{3} - a^{2} + 3 a + 1\) , \( a^{2} - 1\) , \( -1624209 a^{3} - 1343372 a^{2} + 4042371 a + 888957\) , \( 1544603558 a^{3} + 1277527564 a^{2} - 3844255227 a - 845389548\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+3a+1\right){x}^{2}+\left(-1624209a^{3}-1343372a^{2}+4042371a+888957\right){x}+1544603558a^{3}+1277527564a^{2}-3844255227a-845389548$ |
| 841.7-a4 |
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 |
\( 16554983445 a^{3} - 49664950335 a + 26786530035 \) |
\( \bigl[a^{3} - 3 a\) , \( -a + 1\) , \( a^{3} - 2 a + 1\) , \( -326 a^{3} - 213 a^{2} + 849 a + 27\) , \( -3635 a^{3} - 3265 a^{2} + 8894 a + 2657\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-2a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-326a^{3}-213a^{2}+849a+27\right){x}-3635a^{3}-3265a^{2}+8894a+2657$ |
| 841.8-a6 |
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 |
\( 16554983445 a^{3} - 49664950335 a + 26786530035 \) |
\( \bigl[a\) , \( a^{2} - a - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -6055524 a^{3} - 5008513 a^{2} + 15071068 a + 3314280\) , \( -11131060964 a^{3} - 9206399587 a^{2} + 27703314743 a + 6092231498\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-3a-1\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-6055524a^{3}-5008513a^{2}+15071068a+3314280\right){x}-11131060964a^{3}-9206399587a^{2}+27703314743a+6092231498$ |
| 841.8-a8 |
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 |
\( 16554983445 a^{3} - 49664950335 a + 26786530035 \) |
\( \bigl[1\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a^{2} + a - 2\) , \( -1125 a^{3} - 897 a^{2} + 2819 a + 527\) , \( 27556 a^{3} + 22887 a^{2} - 68523 a - 15332\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-3\right){x}^{2}+\left(-1125a^{3}-897a^{2}+2819a+527\right){x}+27556a^{3}+22887a^{2}-68523a-15332$ |
| 841.9-a2 |
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 |
\( 16554983445 a^{3} - 49664950335 a + 26786530035 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 2 a - 2\) , \( a^{2} - 2\) , \( -4656162 a^{3} - 3851083 a^{2} + 11588363 a + 2548394\) , \( -7511798086 a^{3} - 6212939993 a^{2} + 18695586113 a + 4111343335\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-2a-2\right){x}^{2}+\left(-4656162a^{3}-3851083a^{2}+11588363a+2548394\right){x}-7511798086a^{3}-6212939993a^{2}+18695586113a+4111343335$ |
| 841.9-a7 |
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 |
\( 16554983445 a^{3} - 49664950335 a + 26786530035 \) |
\( \bigl[a + 1\) , \( a^{2} - 3\) , \( a^{3} - 3 a\) , \( -4 a^{3} - 7 a^{2} - 2 a - 16\) , \( 10 a^{3} + 27 a^{2} + 14 a - 12\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-4a^{3}-7a^{2}-2a-16\right){x}+10a^{3}+27a^{2}+14a-12$ |
| 961.10-b2 |
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] |
$1$ |
\( 2 \) |
$0.333651787$ |
$129.4181277$ |
2.574792903 |
\( 16554983445 a^{3} - 49664950335 a + 26786530035 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} - 3\) , \( a + 1\) , \( -13246251 a^{3} - 10955859 a^{2} + 32967653 a + 7249914\) , \( 36003341430 a^{3} + 29778036624 a^{2} - 89606185527 a - 19705281836\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-13246251a^{3}-10955859a^{2}+32967653a+7249914\right){x}+36003341430a^{3}+29778036624a^{2}-89606185527a-19705281836$ |
| 961.10-b8 |
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] |
$1$ |
\( 2 \) |
$0.556086312$ |
$77.65087667$ |
2.574792903 |
\( 16554983445 a^{3} - 49664950335 a + 26786530035 \) |
\( \bigl[a + 1\) , \( -a^{3} + 4 a\) , \( a^{3} - 2 a\) , \( -47 a^{3} - 48 a^{2} + 125 a + 24\) , \( -314 a^{3} - 286 a^{2} + 788 a + 178\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-2a\right){y}={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(-47a^{3}-48a^{2}+125a+24\right){x}-314a^{3}-286a^{2}+788a+178$ |
| 961.7-b1 |
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] |
$1$ |
\( 2 \) |
$0.111217262$ |
$388.2543833$ |
2.574792903 |
\( 16554983445 a^{3} - 49664950335 a + 26786530035 \) |
\( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{2} + a - 2\) , \( -742 a^{3} + 466 a^{2} + 2513 a - 2417\) , \( 13104 a^{3} - 11905 a^{2} - 46670 a + 52371\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+3a-1\right){x}^{2}+\left(-742a^{3}+466a^{2}+2513a-2417\right){x}+13104a^{3}-11905a^{2}-46670a+52371$ |
| 961.7-b8 |
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] |
$1$ |
\( 2 \) |
$1.668258938$ |
$25.88362555$ |
2.574792903 |
\( 16554983445 a^{3} - 49664950335 a + 26786530035 \) |
\( \bigl[1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( 1\) , \( -1158278 a^{3} - 958000 a^{2} + 2882755 a + 633942\) , \( -931622486 a^{3} - 770536492 a^{2} + 2318649718 a + 509893883\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(-1158278a^{3}-958000a^{2}+2882755a+633942\right){x}-931622486a^{3}-770536492a^{2}+2318649718a+509893883$ |
| 961.8-b3 |
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] |
$1$ |
\( 2 \) |
$0.333651787$ |
$129.4181277$ |
2.574792903 |
\( 16554983445 a^{3} - 49664950335 a + 26786530035 \) |
\( \bigl[a^{2} + a - 1\) , \( -a^{2} - a + 1\) , \( a^{3} + a^{2} - 2 a - 2\) , \( -30 a^{3} - 5 a^{2} + 107 a - 63\) , \( -10 a^{3} - 73 a^{2} - 69 a + 248\bigr] \) |
${y}^2+\left(a^{2}+a-1\right){x}{y}+\left(a^{3}+a^{2}-2a-2\right){y}={x}^{3}+\left(-a^{2}-a+1\right){x}^{2}+\left(-30a^{3}-5a^{2}+107a-63\right){x}-10a^{3}-73a^{2}-69a+248$ |
| 961.8-b6 |
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] |
$1$ |
\( 2 \) |
$0.556086312$ |
$77.65087667$ |
2.574792903 |
\( 16554983445 a^{3} - 49664950335 a + 26786530035 \) |
\( \bigl[a^{3} - 2 a\) , \( a^{2} + a - 2\) , \( a^{2} + a - 1\) , \( -4038928 a^{3} - 3340559 a^{2} + 10052203 a + 2210575\) , \( 6056496764 a^{3} + 5009273452 a^{2} - 15073589041 a - 3314830541\bigr] \) |
${y}^2+\left(a^{3}-2a\right){x}{y}+\left(a^{2}+a-1\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(-4038928a^{3}-3340559a^{2}+10052203a+2210575\right){x}+6056496764a^{3}+5009273452a^{2}-15073589041a-3314830541$ |
| 961.9-b5 |
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] |
$1$ |
\( 2 \) |
$0.111217262$ |
$388.2543833$ |
2.574792903 |
\( 16554983445 a^{3} - 49664950335 a + 26786530035 \) |
\( \bigl[a^{3} + a^{2} - 2 a - 1\) , \( -a + 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -917 a^{3} - 463 a^{2} + 2463 a - 272\) , \( 16332 a^{3} + 10420 a^{2} - 42556 a - 853\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-2a-1\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-917a^{3}-463a^{2}+2463a-272\right){x}+16332a^{3}+10420a^{2}-42556a-853$ |
| 961.9-b8 |
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] |
$1$ |
\( 2 \) |
$1.668258938$ |
$25.88362555$ |
2.574792903 |
\( 16554983445 a^{3} - 49664950335 a + 26786530035 \) |
\( \bigl[a + 1\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( 1\) , \( -4224272 a^{3} - 3493908 a^{2} + 10513374 a + 2311997\) , \( -6487761039 a^{3} - 5365968522 a^{2} + 16146931708 a + 3550869173\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a^{3}+a^{2}+2a-1\right){x}^{2}+\left(-4224272a^{3}-3493908a^{2}+10513374a+2311997\right){x}-6487761039a^{3}-5365968522a^{2}+16146931708a+3550869173$ |
*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.
