| Label |
Cremona label |
Class |
Cremona class |
Class size |
Class degree |
Conductor |
Discriminant |
Rank |
Torsion |
$\textrm{End}^0(E_{\overline\Q})$ |
CM |
Sato-Tate |
Semistable |
Potentially good |
Nonmax $\ell$ |
$\ell$-adic images |
mod-$\ell$ images |
Adelic level |
Adelic index |
Adelic genus |
Regulator |
$Ш_{\textrm{an}}$ |
Ш primes |
Integral points |
Modular degree |
Faltings height |
j-invariant |
$abc$ quality |
Szpiro ratio |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
| 90.a1 |
90a4 |
90.a |
90a |
$4$ |
$6$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
\( 2^{3} \cdot 3^{9} \cdot 5^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.8.0.2 |
2B, 3B.1.2 |
$120$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$48$ |
$0.377518$ |
$8527173507/200$ |
$1.05154$ |
$7.27898$ |
$[1, -1, 0, -1149, -14707]$ |
\(y^2+xy=x^3-x^2-1149x-14707\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 24.48.0-24.ca.1.7, 40.6.0.e.1, $\ldots$ |
$[]$ |
| 90.a2 |
90a3 |
90.a |
90a |
$4$ |
$6$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
\( - 2^{6} \cdot 3^{9} \cdot 5 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.8.0.2 |
2B, 3B.1.2 |
$120$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$24$ |
$0.030944$ |
$-1860867/320$ |
$0.97305$ |
$5.46339$ |
$[1, -1, 0, -69, -235]$ |
\(y^2+xy=x^3-x^2-69x-235\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 24.48.0-24.cd.1.11, 30.48.0-30.b.1.3, $\ldots$ |
$[]$ |
| 90.a3 |
90a2 |
90.a |
90a |
$4$ |
$6$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
\( 2 \cdot 3^{3} \cdot 5^{6} \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.8.0.1 |
2B, 3B.1.1 |
$120$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$4$ |
$16$ |
$-0.171788$ |
$57960603/31250$ |
$1.11205$ |
$4.70489$ |
$[1, -1, 0, -24, 18]$ |
\(y^2+xy=x^3-x^2-24x+18\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 24.48.0-24.ca.1.15, 40.6.0.e.1, $\ldots$ |
$[]$ |
| 90.a4 |
90a1 |
90.a |
90a |
$4$ |
$6$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
\( - 2^{2} \cdot 3^{3} \cdot 5^{3} \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.8.0.1 |
2B, 3B.1.1 |
$120$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$5$ |
$8$ |
$-0.518362$ |
$804357/500$ |
$1.08207$ |
$3.75430$ |
$[1, -1, 0, 6, 0]$ |
\(y^2+xy=x^3-x^2+6x\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 24.48.0-24.cd.1.15, 30.48.0-30.b.1.4, $\ldots$ |
$[]$ |
| 90.b1 |
90b4 |
90.b |
90b |
$4$ |
$6$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
\( 2 \cdot 3^{9} \cdot 5^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.8.0.2 |
2B, 3B.1.2 |
$120$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$48$ |
$0.377518$ |
$57960603/31250$ |
$1.11205$ |
$6.16977$ |
$[1, -1, 1, -218, -269]$ |
\(y^2+xy+y=x^3-x^2-218x-269\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 24.48.0-24.ca.1.7, 40.6.0.e.1, $\ldots$ |
$[]$ |
| 90.b2 |
90b2 |
90.b |
90b |
$4$ |
$6$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
\( 2^{3} \cdot 3^{3} \cdot 5^{2} \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.8.0.1 |
2B, 3B.1.1 |
$120$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$4$ |
$16$ |
$-0.171788$ |
$8527173507/200$ |
$1.05154$ |
$5.81410$ |
$[1, -1, 1, -128, 587]$ |
\(y^2+xy+y=x^3-x^2-128x+587\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 24.48.0-24.ca.1.15, 40.6.0.e.1, $\ldots$ |
$[]$ |
| 90.b3 |
90b1 |
90.b |
90b |
$4$ |
$6$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
\( - 2^{6} \cdot 3^{3} \cdot 5 \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.8.0.1 |
2B, 3B.1.1 |
$120$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$5$ |
$8$ |
$-0.518362$ |
$-1860867/320$ |
$0.97305$ |
$3.99852$ |
$[1, -1, 1, -8, 11]$ |
\(y^2+xy+y=x^3-x^2-8x+11\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 6.24.0-6.a.1.4, 24.48.0-24.cd.1.15, 30.48.0-30.b.1.4, $\ldots$ |
$[]$ |
| 90.b4 |
90b3 |
90.b |
90b |
$4$ |
$6$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
\( - 2^{2} \cdot 3^{9} \cdot 5^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
2.3.0.1, 3.8.0.2 |
2B, 3B.1.2 |
$120$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$24$ |
$0.030944$ |
$804357/500$ |
$1.08207$ |
$5.21918$ |
$[1, -1, 1, 52, -53]$ |
\(y^2+xy+y=x^3-x^2+52x-53\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 6.24.0-6.a.1.2, 24.48.0-24.cd.1.11, 30.48.0-30.b.1.3, $\ldots$ |
$[]$ |
| 90.c1 |
90c8 |
90.c |
90c |
$8$ |
$12$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
\( 2^{3} \cdot 3^{10} \cdot 5^{3} \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.12.0.6, 3.8.0.1 |
2B, 3B.1.1 |
$120$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$4$ |
$192$ |
$1.113472$ |
$16778985534208729/81000$ |
$1.08181$ |
$9.76721$ |
$[1, -1, 1, -48002, 4059929]$ |
\(y^2+xy+y=x^3-x^2-48002x+4059929\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 4.6.0.c.1, 6.24.0-6.a.1.4, 8.12.0-4.c.1.5, $\ldots$ |
$[]$ |
| 90.c2 |
90c7 |
90.c |
90c |
$8$ |
$12$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
\( 2^{3} \cdot 3^{7} \cdot 5^{12} \) |
$0$ |
$\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.12.0.8, 3.8.0.1 |
2B, 3B.1.1 |
$120$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$4$ |
$192$ |
$1.113472$ |
$10316097499609/5859375000$ |
$1.13600$ |
$8.12399$ |
$[1, -1, 1, -4082, 14681]$ |
\(y^2+xy+y=x^3-x^2-4082x+14681\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 4.12.0-4.c.1.2, 6.24.0-6.a.1.4, 12.96.0-12.c.3.7, $\ldots$ |
$[]$ |
| 90.c3 |
90c6 |
90.c |
90c |
$8$ |
$12$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
\( 2^{6} \cdot 3^{8} \cdot 5^{6} \) |
$0$ |
$\Z/2\Z\oplus\Z/6\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.12.0.1, 3.8.0.1 |
2Cs, 3B.1.1 |
$120$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$10$ |
$96$ |
$0.766898$ |
$4102915888729/9000000$ |
$1.05221$ |
$7.91909$ |
$[1, -1, 1, -3002, 63929]$ |
\(y^2+xy+y=x^3-x^2-3002x+63929\) |
2.6.0.a.1, 3.8.0-3.a.1.2, 4.12.0-2.a.1.1, 6.48.0-6.a.1.1, 12.96.0-12.a.1.7, $\ldots$ |
$[]$ |
| 90.c4 |
90c4 |
90.c |
90c |
$8$ |
$12$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
\( 2 \cdot 3^{9} \cdot 5^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.12.0.8, 3.8.0.2 |
2B, 3B.1.2 |
$120$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$0$ |
$64$ |
$0.564166$ |
$2656166199049/33750$ |
$1.05017$ |
$7.82246$ |
$[1, -1, 1, -2597, -50281]$ |
\(y^2+xy+y=x^3-x^2-2597x-50281\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 4.12.0-4.c.1.2, 6.24.0-6.a.1.2, 12.96.0-12.c.4.6, $\ldots$ |
$[]$ |
| 90.c5 |
90c5 |
90.c |
90c |
$8$ |
$12$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
\( 2 \cdot 3^{18} \cdot 5 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.12.0.6, 3.8.0.2 |
2B, 3B.1.2 |
$120$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$0$ |
$64$ |
$0.564166$ |
$35578826569/5314410$ |
$1.03393$ |
$6.86400$ |
$[1, -1, 1, -617, 5231]$ |
\(y^2+xy+y=x^3-x^2-617x+5231\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.c.1, 6.24.0-6.a.1.2, 8.12.0-4.c.1.5, $\ldots$ |
$[]$ |
| 90.c6 |
90c2 |
90.c |
90c |
$8$ |
$12$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
\( 2^{2} \cdot 3^{12} \cdot 5^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.12.0.1, 3.8.0.2 |
2Cs, 3B.1.2 |
$120$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$2$ |
$32$ |
$0.217592$ |
$702595369/72900$ |
$1.00457$ |
$5.99180$ |
$[1, -1, 1, -167, -709]$ |
\(y^2+xy+y=x^3-x^2-167x-709\) |
2.6.0.a.1, 3.8.0-3.a.1.1, 4.12.0-2.a.1.1, 6.48.0-6.a.1.2, 12.96.0-12.a.2.15, $\ldots$ |
$[]$ |
| 90.c7 |
90c3 |
90.c |
90c |
$8$ |
$12$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
\( - 2^{12} \cdot 3^{7} \cdot 5^{3} \) |
$0$ |
$\Z/12\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.12.0.7, 3.8.0.1 |
2B, 3B.1.1 |
$120$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$11$ |
$48$ |
$0.420325$ |
$-273359449/1536000$ |
$1.04920$ |
$6.30896$ |
$[1, -1, 1, -122, 1721]$ |
\(y^2+xy+y=x^3-x^2-122x+1721\) |
2.3.0.a.1, 3.8.0-3.a.1.2, 4.12.0-4.c.1.1, 6.24.0-6.a.1.4, 12.96.0-12.c.1.8, $\ldots$ |
$[]$ |
| 90.c8 |
90c1 |
90.c |
90c |
$8$ |
$12$ |
\( 2 \cdot 3^{2} \cdot 5 \) |
\( - 2^{4} \cdot 3^{9} \cdot 5 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.12.0.7, 3.8.0.2 |
2B, 3B.1.2 |
$120$ |
$384$ |
$5$ |
$1$ |
$1$ |
|
$3$ |
$16$ |
$-0.128981$ |
$357911/2160$ |
$0.99689$ |
$4.80541$ |
$[1, -1, 1, 13, -61]$ |
\(y^2+xy+y=x^3-x^2+13x-61\) |
2.3.0.a.1, 3.8.0-3.a.1.1, 4.12.0-4.c.1.1, 6.24.0-6.a.1.2, 12.96.0-12.c.2.8, $\ldots$ |
$[]$ |
