| 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 |
| 825.a1 |
825b3 |
825.a |
825b |
$4$ |
$4$ |
\( 3 \cdot 5^{2} \cdot 11 \) |
\( 3^{3} \cdot 5^{6} \cdot 11^{4} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1320$ |
$48$ |
$0$ |
$0.213608727$ |
$1$ |
|
$10$ |
$768$ |
$0.792087$ |
$347873904937/395307$ |
$1.00913$ |
$5.39533$ |
$[1, 0, 0, -3663, 84942]$ |
\(y^2+xy=x^3-3663x+84942\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0.h.1, 20.12.0-4.c.1.2, 60.24.0-12.h.1.2, $\ldots$ |
$[(33, 0)]$ |
| 825.a2 |
825b2 |
825.a |
825b |
$4$ |
$4$ |
\( 3 \cdot 5^{2} \cdot 11 \) |
\( 3^{6} \cdot 5^{6} \cdot 11^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$660$ |
$48$ |
$0$ |
$0.427217455$ |
$1$ |
|
$18$ |
$384$ |
$0.445513$ |
$169112377/88209$ |
$1.00669$ |
$4.25928$ |
$[1, 0, 0, -288, 567]$ |
\(y^2+xy=x^3-288x+567\) |
2.6.0.a.1, 12.12.0.a.1, 20.12.0-2.a.1.1, 44.12.0.b.1, 60.24.0-12.a.1.1, $\ldots$ |
$[(-9, 54)]$ |
| 825.a3 |
825b1 |
825.a |
825b |
$4$ |
$4$ |
\( 3 \cdot 5^{2} \cdot 11 \) |
\( 3^{3} \cdot 5^{6} \cdot 11 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1320$ |
$48$ |
$0$ |
$0.854434911$ |
$1$ |
|
$7$ |
$192$ |
$0.098940$ |
$30664297/297$ |
$1.09706$ |
$4.00502$ |
$[1, 0, 0, -163, -808]$ |
\(y^2+xy=x^3-163x-808\) |
2.3.0.a.1, 4.6.0.c.1, 24.12.0.ba.1, 40.12.0-4.c.1.5, 60.12.0-4.c.1.2, $\ldots$ |
$[(-7, 5)]$ |
| 825.a4 |
825b4 |
825.a |
825b |
$4$ |
$4$ |
\( 3 \cdot 5^{2} \cdot 11 \) |
\( - 3^{12} \cdot 5^{6} \cdot 11 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$1320$ |
$48$ |
$0$ |
$0.213608727$ |
$1$ |
|
$12$ |
$768$ |
$0.792087$ |
$9090072503/5845851$ |
$1.03763$ |
$4.85260$ |
$[1, 0, 0, 1087, 4692]$ |
\(y^2+xy=x^3+1087x+4692\) |
2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 22.6.0.a.1, 24.12.0.ba.1, $\ldots$ |
$[(7, 109)]$ |
| 825.b1 |
825a1 |
825.b |
825a |
$2$ |
$3$ |
\( 3 \cdot 5^{2} \cdot 11 \) |
\( - 3^{3} \cdot 5^{2} \cdot 11^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$30$ |
$16$ |
$0$ |
$0.267281464$ |
$1$ |
|
$4$ |
$72$ |
$-0.301211$ |
$-56197120/3267$ |
$0.94162$ |
$3.15082$ |
$[0, -1, 1, -23, 53]$ |
\(y^2+y=x^3-x^2-23x+53\) |
3.4.0.a.1, 6.8.0.b.1, 15.8.0-3.a.1.2, 30.16.0-6.b.1.2 |
$[(1, 5)]$ |
| 825.b2 |
825a2 |
825.b |
825a |
$2$ |
$3$ |
\( 3 \cdot 5^{2} \cdot 11 \) |
\( - 3 \cdot 5^{2} \cdot 11^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$30$ |
$16$ |
$0$ |
$0.801844394$ |
$1$ |
|
$4$ |
$216$ |
$0.248095$ |
$8990228480/5314683$ |
$1.15904$ |
$3.89230$ |
$[0, -1, 1, 127, 38]$ |
\(y^2+y=x^3-x^2+127x+38\) |
3.4.0.a.1, 6.8.0.b.1, 15.8.0-3.a.1.1, 30.16.0-6.b.1.1 |
$[(76, 665)]$ |
| 825.c1 |
825c1 |
825.c |
825c |
$2$ |
$3$ |
\( 3 \cdot 5^{2} \cdot 11 \) |
\( - 3^{3} \cdot 5^{8} \cdot 11^{2} \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$6$ |
$16$ |
$0$ |
$0.750802424$ |
$1$ |
|
$8$ |
$360$ |
$0.503509$ |
$-56197120/3267$ |
$0.94162$ |
$4.58881$ |
$[0, 1, 1, -583, 5494]$ |
\(y^2+y=x^3+x^2-583x+5494\) |
3.8.0-3.a.1.2, 6.16.0-6.b.1.2 |
$[(14, 16)]$ |
| 825.c2 |
825c2 |
825.c |
825c |
$2$ |
$3$ |
\( 3 \cdot 5^{2} \cdot 11 \) |
\( - 3 \cdot 5^{8} \cdot 11^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$6$ |
$16$ |
$0$ |
$2.252407273$ |
$1$ |
|
$0$ |
$1080$ |
$1.052814$ |
$8990228480/5314683$ |
$1.15904$ |
$5.33029$ |
$[0, 1, 1, 3167, 11119]$ |
\(y^2+y=x^3+x^2+3167x+11119\) |
3.8.0-3.a.1.1, 6.16.0-6.b.1.1 |
$[(181/2, 3989/2)]$ |
