| 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 |
| 75.a1 |
75c2 |
75.a |
75c |
$2$ |
$5$ |
\( 3 \cdot 5^{2} \) |
\( - 3 \cdot 5^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.24.0.3 |
5B.1.2 |
$30$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$30$ |
$0.211621$ |
$-102400/3$ |
$1.04391$ |
$6.41123$ |
$[0, 1, 1, -208, -1256]$ |
\(y^2+y=x^3+x^2-208x-1256\) |
5.24.0-5.a.2.2, 6.2.0.a.1, 30.48.1-30.d.2.4 |
$[]$ |
| 75.a2 |
75c1 |
75.a |
75c |
$2$ |
$5$ |
\( 3 \cdot 5^{2} \) |
\( - 3^{5} \cdot 5^{2} \) |
$0$ |
$\Z/5\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.24.0.1 |
5B.1.1 |
$30$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$4$ |
$6$ |
$-0.593099$ |
$20480/243$ |
$1.13104$ |
$3.73288$ |
$[0, 1, 1, 2, 4]$ |
\(y^2+y=x^3+x^2+2x+4\) |
5.24.0-5.a.1.2, 6.2.0.a.1, 30.48.1-30.d.1.4 |
$[]$ |
| 75.b1 |
75b7 |
75.b |
75b |
$8$ |
$16$ |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.96.0.168 |
2B |
$480$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$0$ |
$96$ |
$1.095589$ |
$1114544804970241/405$ |
$1.07354$ |
$10.26149$ |
$[1, 0, 1, -54001, -4834477]$ |
\(y^2+xy+y=x^3-54001x-4834477\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.bb.2.6, 10.6.0.a.1, 16.96.0-16.x.2.5, $\ldots$ |
$[]$ |
| 75.b2 |
75b5 |
75.b |
75b |
$8$ |
$16$ |
\( 3 \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{8} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.96.0.31 |
2Cs |
$240$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$2$ |
$48$ |
$0.749015$ |
$272223782641/164025$ |
$1.03897$ |
$8.33506$ |
$[1, 0, 1, -3376, -75727]$ |
\(y^2+xy+y=x^3-3376x-75727\) |
2.6.0.a.1, 4.24.0-4.b.1.2, 8.96.0-8.k.1.7, 20.48.0-20.c.1.3, 40.192.1-40.cc.2.5, $\ldots$ |
$[]$ |
| 75.b3 |
75b8 |
75.b |
75b |
$8$ |
$16$ |
\( 3 \cdot 5^{2} \) |
\( - 3^{16} \cdot 5^{7} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.96.0.121 |
2B |
$480$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$2$ |
$96$ |
$1.095589$ |
$-147281603041/215233605$ |
$1.05949$ |
$8.48461$ |
$[1, 0, 1, -2751, -104477]$ |
\(y^2+xy+y=x^3-2751x-104477\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.ba.2.7, 16.96.0-16.u.2.5, 20.24.0-20.h.1.2, $\ldots$ |
$[]$ |
| 75.b4 |
75b4 |
75.b |
75b |
$8$ |
$16$ |
\( 3 \cdot 5^{2} \) |
\( 3 \cdot 5^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
32.96.0.29 |
2B |
$480$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$0$ |
$24$ |
$0.402442$ |
$56667352321/15$ |
$1.03019$ |
$7.97155$ |
$[1, 0, 1, -2001, 34273]$ |
\(y^2+xy+y=x^3-2001x+34273\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.1, 12.12.0-4.c.1.1, 16.48.0-16.g.1.1, $\ldots$ |
$[]$ |
| 75.b5 |
75b3 |
75.b |
75b |
$8$ |
$16$ |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{10} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.96.0.77 |
2Cs |
$240$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$2$ |
$24$ |
$0.402442$ |
$111284641/50625$ |
$1.02534$ |
$6.52792$ |
$[1, 0, 1, -251, -727]$ |
\(y^2+xy+y=x^3-251x-727\) |
2.6.0.a.1, 4.24.0.b.1, 8.96.0-8.b.2.3, 20.48.0-4.b.1.1, 24.192.1-24.n.1.9, $\ldots$ |
$[]$ |
| 75.b6 |
75b2 |
75.b |
75b |
$8$ |
$16$ |
\( 3 \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{8} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.96.0.35 |
2Cs |
$240$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$2$ |
$12$ |
$0.055868$ |
$13997521/225$ |
$0.96230$ |
$6.04773$ |
$[1, 0, 1, -126, 523]$ |
\(y^2+xy+y=x^3-126x+523\) |
2.6.0.a.1, 4.12.0.b.1, 8.48.0-8.i.1.3, 12.24.0-4.b.1.2, 16.96.0-16.d.2.8, $\ldots$ |
$[]$ |
| 75.b7 |
75b1 |
75.b |
75b |
$8$ |
$16$ |
\( 3 \cdot 5^{2} \) |
\( - 3 \cdot 5^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
32.96.0.29 |
2B |
$480$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$1$ |
$6$ |
$-0.290706$ |
$-1/15$ |
$1.19808$ |
$4.59050$ |
$[1, 0, 1, -1, 23]$ |
\(y^2+xy+y=x^3-x+23\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.n.1.1, 12.12.0-4.c.1.2, 16.48.0-16.g.1.1, $\ldots$ |
$[]$ |
| 75.b8 |
75b6 |
75.b |
75b |
$8$ |
$16$ |
\( 3 \cdot 5^{2} \) |
\( - 3^{2} \cdot 5^{14} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.96.0.197 |
2B |
$480$ |
$768$ |
$13$ |
$1$ |
$1$ |
|
$0$ |
$48$ |
$0.749015$ |
$4733169839/3515625$ |
$1.05585$ |
$7.39654$ |
$[1, 0, 1, 874, -5227]$ |
\(y^2+xy+y=x^3+874x-5227\) |
2.3.0.a.1, 4.12.0.d.1, 8.48.0.n.2, 16.96.0-8.n.2.2, 20.24.0-4.d.1.1, $\ldots$ |
$[]$ |
| 75.c1 |
75a1 |
75.c |
75a |
$2$ |
$5$ |
\( 3 \cdot 5^{2} \) |
\( - 3 \cdot 5^{4} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.24.0.4 |
5B.1.3 |
$30$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$6$ |
$-0.593099$ |
$-102400/3$ |
$1.04391$ |
$4.17460$ |
$[0, -1, 1, -8, -7]$ |
\(y^2+y=x^3-x^2-8x-7\) |
5.24.0-5.a.2.1, 6.2.0.a.1, 30.48.1-30.d.2.3 |
$[]$ |
| 75.c2 |
75a2 |
75.c |
75a |
$2$ |
$5$ |
\( 3 \cdot 5^{2} \) |
\( - 3^{5} \cdot 5^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.24.0.2 |
5B.1.4 |
$30$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$30$ |
$0.211621$ |
$20480/243$ |
$1.13104$ |
$5.96951$ |
$[0, -1, 1, 42, 443]$ |
\(y^2+y=x^3-x^2+42x+443\) |
5.24.0-5.a.1.1, 6.2.0.a.1, 30.48.1-30.d.1.3 |
$[]$ |
