| 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 |
| 350.a1 |
350c2 |
350.a |
350c |
$2$ |
$3$ |
\( 2 \cdot 5^{2} \cdot 7 \) |
\( - 2 \cdot 5^{2} \cdot 7^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.2.0.1, 3.4.0.1 |
3B |
$120$ |
$16$ |
$0$ |
$0.653095700$ |
$1$ |
|
$4$ |
$72$ |
$0.002135$ |
$-417267265/235298$ |
$0.94642$ |
$4.05406$ |
$[1, 1, 0, -45, -185]$ |
\(y^2+xy=x^3+x^2-45x-185\) |
3.4.0.a.1, 8.2.0.a.1, 15.8.0-3.a.1.1, 24.8.0.a.1, 120.16.0.? |
$[(31, 156)]$ |
| 350.a2 |
350c1 |
350.a |
350c |
$2$ |
$3$ |
\( 2 \cdot 5^{2} \cdot 7 \) |
\( - 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.2.0.1, 3.4.0.1 |
3B |
$120$ |
$16$ |
$0$ |
$0.217698566$ |
$1$ |
|
$6$ |
$24$ |
$-0.547172$ |
$397535/392$ |
$1.09655$ |
$2.75044$ |
$[1, 1, 0, 5, 5]$ |
\(y^2+xy=x^3+x^2+5x+5\) |
3.4.0.a.1, 8.2.0.a.1, 15.8.0-3.a.1.2, 24.8.0.a.1, 120.16.0.? |
$[(1, 3)]$ |
| 350.b1 |
350a3 |
350.b |
350a |
$4$ |
$4$ |
\( 2 \cdot 5^{2} \cdot 7 \) |
\( 2 \cdot 5^{8} \cdot 7^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.15 |
2B |
$280$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$384$ |
$0.843707$ |
$2121328796049/120050$ |
$1.01959$ |
$6.49371$ |
$[1, -1, 0, -6692, -209034]$ |
\(y^2+xy=x^3-x^2-6692x-209034\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 20.12.0-4.c.1.1, 40.24.0-8.k.1.1, $\ldots$ |
$[]$ |
| 350.b2 |
350a4 |
350.b |
350a |
$4$ |
$4$ |
\( 2 \cdot 5^{2} \cdot 7 \) |
\( 2 \cdot 5^{14} \cdot 7 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.9 |
2B |
$280$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$384$ |
$0.843707$ |
$74565301329/5468750$ |
$0.99962$ |
$5.92215$ |
$[1, -1, 0, -2192, 37466]$ |
\(y^2+xy=x^3-x^2-2192x+37466\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 40.24.0-8.p.1.4, 56.24.0.bp.1, $\ldots$ |
$[]$ |
| 350.b3 |
350a2 |
350.b |
350a |
$4$ |
$4$ |
\( 2 \cdot 5^{2} \cdot 7 \) |
\( 2^{2} \cdot 5^{10} \cdot 7^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.3 |
2Cs |
$280$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$192$ |
$0.497133$ |
$611960049/122500$ |
$1.02632$ |
$5.10228$ |
$[1, -1, 0, -442, -2784]$ |
\(y^2+xy=x^3-x^2-442x-2784\) |
2.6.0.a.1, 8.12.0.a.1, 20.12.0-2.a.1.1, 28.12.0.b.1, 40.24.0-8.a.1.2, $\ldots$ |
$[]$ |
| 350.b4 |
350a1 |
350.b |
350a |
$4$ |
$4$ |
\( 2 \cdot 5^{2} \cdot 7 \) |
\( - 2^{4} \cdot 5^{8} \cdot 7 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.9 |
2B |
$280$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$96$ |
$0.150559$ |
$1367631/2800$ |
$1.00023$ |
$4.21932$ |
$[1, -1, 0, 58, -284]$ |
\(y^2+xy=x^3-x^2+58x-284\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 14.6.0.b.1, 20.12.0-4.c.1.2, $\ldots$ |
$[]$ |
| 350.c1 |
350e1 |
350.c |
350e |
$1$ |
$1$ |
\( 2 \cdot 5^{2} \cdot 7 \) |
\( - 2^{11} \cdot 5^{10} \cdot 7^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.2.0.1 |
|
$8$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$1320$ |
$1.041822$ |
$-1026590625/100352$ |
$1.12597$ |
$6.31622$ |
$[1, -1, 0, -4492, 126416]$ |
\(y^2+xy=x^3-x^2-4492x+126416\) |
8.2.0.a.1 |
$[]$ |
| 350.d1 |
350f1 |
350.d |
350f |
$1$ |
$1$ |
\( 2 \cdot 5^{2} \cdot 7 \) |
\( - 2^{11} \cdot 5^{4} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.2.0.1 |
|
$8$ |
$2$ |
$0$ |
$0.012846808$ |
$1$ |
|
$24$ |
$264$ |
$0.237103$ |
$-1026590625/100352$ |
$1.12597$ |
$4.66774$ |
$[1, -1, 1, -180, 1047]$ |
\(y^2+xy+y=x^3-x^2-180x+1047\) |
8.2.0.a.1 |
$[(-1, 35)]$ |
| 350.e1 |
350b2 |
350.e |
350b |
$2$ |
$3$ |
\( 2 \cdot 5^{2} \cdot 7 \) |
\( - 2 \cdot 5^{8} \cdot 7^{6} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.2.0.1, 3.8.0.2 |
3B.1.2 |
$24$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$360$ |
$0.806853$ |
$-417267265/235298$ |
$0.94642$ |
$5.70253$ |
$[1, 0, 0, -1138, -20858]$ |
\(y^2+xy=x^3-1138x-20858\) |
3.8.0-3.a.1.1, 8.2.0.a.1, 24.16.0-24.a.1.6 |
$[]$ |
| 350.e2 |
350b1 |
350.e |
350b |
$2$ |
$3$ |
\( 2 \cdot 5^{2} \cdot 7 \) |
\( - 2^{3} \cdot 5^{8} \cdot 7^{2} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.2.0.1, 3.8.0.1 |
3B.1.1 |
$24$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$120$ |
$0.257547$ |
$397535/392$ |
$1.09655$ |
$4.39891$ |
$[1, 0, 0, 112, 392]$ |
\(y^2+xy=x^3+112x+392\) |
3.8.0-3.a.1.2, 8.2.0.a.1, 24.16.0-24.a.1.8 |
$[]$ |
| 350.f1 |
350d6 |
350.f |
350d |
$6$ |
$18$ |
\( 2 \cdot 5^{2} \cdot 7 \) |
\( 2^{9} \cdot 5^{6} \cdot 7^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 9.12.0.1 |
2B, 3B |
$2520$ |
$864$ |
$21$ |
$1$ |
$1$ |
|
$0$ |
$864$ |
$1.217819$ |
$2251439055699625/25088$ |
$1.06489$ |
$7.68308$ |
$[1, 1, 1, -68263, -6893219]$ |
\(y^2+xy+y=x^3+x^2-68263x-6893219\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 9.12.0.a.1, $\ldots$ |
$[]$ |
| 350.f2 |
350d5 |
350.f |
350d |
$6$ |
$18$ |
\( 2 \cdot 5^{2} \cdot 7 \) |
\( - 2^{18} \cdot 5^{6} \cdot 7 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 9.12.0.1 |
2B, 3B |
$2520$ |
$864$ |
$21$ |
$1$ |
$1$ |
|
$1$ |
$432$ |
$0.871246$ |
$-548347731625/1835008$ |
$1.02933$ |
$6.26374$ |
$[1, 1, 1, -4263, -109219]$ |
\(y^2+xy+y=x^3+x^2-4263x-109219\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 9.12.0.a.1, $\ldots$ |
$[]$ |
| 350.f3 |
350d4 |
350.f |
350d |
$6$ |
$18$ |
\( 2 \cdot 5^{2} \cdot 7 \) |
\( 2^{3} \cdot 5^{6} \cdot 7^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 3.12.0.1 |
2B, 3Cs |
$2520$ |
$864$ |
$21$ |
$1$ |
$1$ |
|
$0$ |
$288$ |
$0.668514$ |
$4956477625/941192$ |
$1.00821$ |
$5.45936$ |
$[1, 1, 1, -888, -8719]$ |
\(y^2+xy+y=x^3+x^2-888x-8719\) |
2.3.0.a.1, 3.12.0.a.1, 6.36.0.a.1, 8.6.0.b.1, 15.24.0-3.a.1.1, $\ldots$ |
$[]$ |
| 350.f4 |
350d2 |
350.f |
350d |
$6$ |
$18$ |
\( 2 \cdot 5^{2} \cdot 7 \) |
\( 2 \cdot 5^{6} \cdot 7^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.6, 9.12.0.1 |
2B, 3B |
$2520$ |
$864$ |
$21$ |
$1$ |
$1$ |
|
$0$ |
$96$ |
$0.119208$ |
$128787625/98$ |
$0.96763$ |
$4.83623$ |
$[1, 1, 1, -263, 1531]$ |
\(y^2+xy+y=x^3+x^2-263x+1531\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.b.1, 9.12.0.a.1, $\ldots$ |
$[]$ |
| 350.f5 |
350d1 |
350.f |
350d |
$6$ |
$18$ |
\( 2 \cdot 5^{2} \cdot 7 \) |
\( - 2^{2} \cdot 5^{6} \cdot 7 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 9.12.0.1 |
2B, 3B |
$2520$ |
$864$ |
$21$ |
$1$ |
$1$ |
|
$1$ |
$48$ |
$-0.227366$ |
$-15625/28$ |
$1.01712$ |
$3.53767$ |
$[1, 1, 1, -13, 31]$ |
\(y^2+xy+y=x^3+x^2-13x+31\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.c.1, 9.12.0.a.1, $\ldots$ |
$[]$ |
| 350.f6 |
350d3 |
350.f |
350d |
$6$ |
$18$ |
\( 2 \cdot 5^{2} \cdot 7 \) |
\( - 2^{6} \cdot 5^{6} \cdot 7^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.1, 3.12.0.1 |
2B, 3Cs |
$2520$ |
$864$ |
$21$ |
$1$ |
$1$ |
|
$1$ |
$144$ |
$0.321940$ |
$9938375/21952$ |
$0.98695$ |
$4.57570$ |
$[1, 1, 1, 112, -719]$ |
\(y^2+xy+y=x^3+x^2+112x-719\) |
2.3.0.a.1, 3.12.0.a.1, 6.36.0.a.1, 8.6.0.c.1, 14.6.0.b.1, $\ldots$ |
$[]$ |
