| 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 |
Manin constant |
| 99.a1 |
99a2 |
99.a |
99a |
$2$ |
$2$ |
\( 3^{2} \cdot 11 \) |
\( 3^{3} \cdot 11^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$132$ |
$12$ |
$0$ |
$0.151285692$ |
$1$ |
|
$10$ |
$8$ |
$-0.488690$ |
$19034163/121$ |
$0.94120$ |
$4.36497$ |
$[1, -1, 1, -17, 30]$ |
\(y^2+xy+y=x^3-x^2-17x+30\) |
2.3.0.a.1, 12.6.0.a.1, 44.6.0.e.1, 132.12.0.? |
$[(0, 5)]$ |
$1$ |
| 99.a2 |
99a1 |
99.a |
99a |
$2$ |
$2$ |
\( 3^{2} \cdot 11 \) |
\( 3^{3} \cdot 11 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$132$ |
$12$ |
$0$ |
$0.302571384$ |
$1$ |
|
$9$ |
$4$ |
$-0.835264$ |
$19683/11$ |
$1.13667$ |
$2.86899$ |
$[1, -1, 1, -2, 0]$ |
\(y^2+xy+y=x^3-x^2-2x\) |
2.3.0.a.1, 12.6.0.b.1, 44.6.0.e.1, 66.6.0.a.1, 132.12.0.? |
$[(0, 0)]$ |
$1$ |
| 99.b1 |
99b3 |
99.b |
99b |
$4$ |
$4$ |
\( 3^{2} \cdot 11 \) |
\( 3^{9} \cdot 11^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.8 |
2B |
$264$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$48$ |
$0.536674$ |
$347873904937/395307$ |
$1.00913$ |
$7.21783$ |
$[1, -1, 1, -1319, -18084]$ |
\(y^2+xy+y=x^3-x^2-1319x-18084\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 12.24.0-12.h.1.1, 88.24.0.?, 264.48.0.? |
$[ ]$ |
$1$ |
| 99.b2 |
99b2 |
99.b |
99b |
$4$ |
$4$ |
\( 3^{2} \cdot 11 \) |
\( 3^{12} \cdot 11^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.1 |
2Cs |
$132$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$24$ |
$0.190100$ |
$169112377/88209$ |
$1.00669$ |
$5.55758$ |
$[1, -1, 1, -104, -102]$ |
\(y^2+xy+y=x^3-x^2-104x-102\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.a.1.2, 44.24.0-44.b.1.3, 132.48.0.? |
$[ ]$ |
$1$ |
| 99.b3 |
99b1 |
99.b |
99b |
$4$ |
$4$ |
\( 3^{2} \cdot 11 \) |
\( 3^{9} \cdot 11 \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.7 |
2B |
$264$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$12$ |
$-0.156473$ |
$30664297/297$ |
$1.09706$ |
$5.18600$ |
$[1, -1, 1, -59, 186]$ |
\(y^2+xy+y=x^3-x^2-59x+186\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.ba.1.8, 66.6.0.a.1, 88.24.0.?, $\ldots$ |
$[ ]$ |
$1$ |
| 99.b4 |
99b4 |
99.b |
99b |
$4$ |
$4$ |
\( 3^{2} \cdot 11 \) |
\( - 3^{18} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.6 |
2B |
$264$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$48$ |
$0.536674$ |
$9090072503/5845851$ |
$1.03763$ |
$6.42467$ |
$[1, -1, 1, 391, -1092]$ |
\(y^2+xy+y=x^3-x^2+391x-1092\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.1, 22.6.0.a.1, $\ldots$ |
$[ ]$ |
$1$ |
| 99.c1 |
99c2 |
99.c |
99c |
$2$ |
$2$ |
\( 3^{2} \cdot 11 \) |
\( 3^{9} \cdot 11^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$132$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$24$ |
$0.060616$ |
$19034163/121$ |
$0.94120$ |
$5.79947$ |
$[1, -1, 0, -150, -667]$ |
\(y^2+xy=x^3-x^2-150x-667\) |
2.3.0.a.1, 12.6.0.a.1, 44.6.0.e.1, 132.12.0.? |
$[ ]$ |
$1$ |
| 99.c2 |
99c1 |
99.c |
99c |
$2$ |
$2$ |
\( 3^{2} \cdot 11 \) |
\( 3^{9} \cdot 11 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$132$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$12$ |
$-0.285958$ |
$19683/11$ |
$1.13667$ |
$4.30348$ |
$[1, -1, 0, -15, 8]$ |
\(y^2+xy=x^3-x^2-15x+8\) |
2.3.0.a.1, 12.6.0.b.1, 44.6.0.e.1, 66.6.0.a.1, 132.12.0.? |
$[ ]$ |
$1$ |
| 99.d1 |
99d3 |
99.d |
99d |
$3$ |
$25$ |
\( 3^{2} \cdot 11 \) |
\( - 3^{6} \cdot 11 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
25.60.0.2 |
5B.4.2 |
$1650$ |
$1200$ |
$37$ |
$1$ |
$1$ |
|
$0$ |
$150$ |
$1.046015$ |
$-52893159101157376/11$ |
$1.09296$ |
$9.81448$ |
$[0, 0, 1, -70383, 7187035]$ |
\(y^2+y=x^3-70383x+7187035\) |
5.12.0.a.2, 15.24.0-5.a.2.1, 22.2.0.a.1, 25.60.0.a.2, 75.120.0.?, $\ldots$ |
$[ ]$ |
$1$ |
| 99.d2 |
99d2 |
99.d |
99d |
$3$ |
$25$ |
\( 3^{2} \cdot 11 \) |
\( - 3^{6} \cdot 11^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.60.0.1 |
5Cs.4.1 |
$1650$ |
$1200$ |
$37$ |
$1$ |
$1$ |
|
$0$ |
$30$ |
$0.241296$ |
$-122023936/161051$ |
$1.01300$ |
$5.74511$ |
$[0, 0, 1, -93, 625]$ |
\(y^2+y=x^3-93x+625\) |
5.60.0.a.1, 15.120.0-5.a.1.1, 22.2.0.a.1, 110.120.5.?, 275.300.12.?, $\ldots$ |
$[ ]$ |
$1$ |
| 99.d3 |
99d1 |
99.d |
99d |
$3$ |
$25$ |
\( 3^{2} \cdot 11 \) |
\( - 3^{6} \cdot 11 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
25.60.0.1 |
5B.4.1 |
$1650$ |
$1200$ |
$37$ |
$1$ |
$1$ |
|
$0$ |
$6$ |
$-0.563422$ |
$-4096/11$ |
$0.82546$ |
$3.62111$ |
$[0, 0, 1, -3, -5]$ |
\(y^2+y=x^3-3x-5\) |
5.12.0.a.1, 15.24.0-5.a.1.1, 22.2.0.a.1, 25.60.0.a.1, 75.120.0.?, $\ldots$ |
$[ ]$ |
$1$ |
