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 |
Regulator |
$Ш_{\textrm{an}}$ |
Ш primes |
Integral points |
Modular degree |
Faltings height |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
1400.a1 |
1400h2 |
1400.a |
1400h |
$2$ |
$2$ |
\( 2^{3} \cdot 5^{2} \cdot 7 \) |
\( 2^{11} \cdot 5^{6} \cdot 7^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$1$ |
$1$ |
|
$1$ |
$640$ |
$0.570050$ |
$3543122/49$ |
$[0, 1, 0, -1008, -12512]$ |
\(y^2=x^3+x^2-1008x-12512\) |
1400.a2 |
1400h1 |
1400.a |
1400h |
$2$ |
$2$ |
\( 2^{3} \cdot 5^{2} \cdot 7 \) |
\( - 2^{10} \cdot 5^{6} \cdot 7 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.1 |
2B |
$1$ |
$1$ |
|
$1$ |
$320$ |
$0.223477$ |
$-4/7$ |
$[0, 1, 0, -8, -512]$ |
\(y^2=x^3+x^2-8x-512\) |
1400.b1 |
1400n1 |
1400.b |
1400n |
$1$ |
$1$ |
\( 2^{3} \cdot 5^{2} \cdot 7 \) |
\( - 2^{4} \cdot 5^{4} \cdot 7 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$0.106620360$ |
$1$ |
|
$8$ |
$144$ |
$-0.375566$ |
$-6400/7$ |
$[0, 1, 0, -8, 13]$ |
\(y^2=x^3+x^2-8x+13\) |
1400.c1 |
1400k1 |
1400.c |
1400k |
$1$ |
$1$ |
\( 2^{3} \cdot 5^{2} \cdot 7 \) |
\( - 2^{4} \cdot 5^{2} \cdot 7^{5} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$0.213996967$ |
$1$ |
|
$6$ |
$240$ |
$-0.002440$ |
$-6288640/16807$ |
$[0, 1, 0, -28, -147]$ |
\(y^2=x^3+x^2-28x-147\) |
1400.d1 |
1400f1 |
1400.d |
1400f |
$1$ |
$1$ |
\( 2^{3} \cdot 5^{2} \cdot 7 \) |
\( - 2^{8} \cdot 5^{3} \cdot 7^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$0.055830152$ |
$1$ |
|
$12$ |
$192$ |
$0.030070$ |
$1024/343$ |
$[0, -1, 0, 7, 157]$ |
\(y^2=x^3-x^2+7x+157\) |
1400.e1 |
1400b1 |
1400.e |
1400b |
$1$ |
$1$ |
\( 2^{3} \cdot 5^{2} \cdot 7 \) |
\( - 2^{11} \cdot 5^{2} \cdot 7^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.2.0.1 |
|
$1$ |
$1$ |
|
$0$ |
$288$ |
$0.077476$ |
$-10303010/49$ |
$[0, -1, 0, -168, -788]$ |
\(y^2=x^3-x^2-168x-788\) |
1400.f1 |
1400g1 |
1400.f |
1400g |
$1$ |
$1$ |
\( 2^{3} \cdot 5^{2} \cdot 7 \) |
\( - 2^{4} \cdot 5^{10} \cdot 7^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$720$ |
$0.743211$ |
$172800/343$ |
$[0, 0, 0, 625, 9375]$ |
\(y^2=x^3+625x+9375\) |
1400.g1 |
1400a4 |
1400.g |
1400a |
$4$ |
$4$ |
\( 2^{3} \cdot 5^{2} \cdot 7 \) |
\( 2^{11} \cdot 5^{6} \cdot 7 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.9 |
2B |
$1$ |
$1$ |
|
$1$ |
$1024$ |
$0.802686$ |
$1443468546/7$ |
$[0, 0, 0, -7475, 248750]$ |
\(y^2=x^3-7475x+248750\) |
1400.g2 |
1400a3 |
1400.g |
1400a |
$4$ |
$4$ |
\( 2^{3} \cdot 5^{2} \cdot 7 \) |
\( 2^{11} \cdot 5^{6} \cdot 7^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.15 |
2B |
$1$ |
$1$ |
|
$1$ |
$1024$ |
$0.802686$ |
$11090466/2401$ |
$[0, 0, 0, -1475, -17250]$ |
\(y^2=x^3-1475x-17250\) |
1400.g3 |
1400a2 |
1400.g |
1400a |
$4$ |
$4$ |
\( 2^{3} \cdot 5^{2} \cdot 7 \) |
\( 2^{10} \cdot 5^{6} \cdot 7^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.3 |
2Cs |
$1$ |
$1$ |
|
$3$ |
$512$ |
$0.456112$ |
$740772/49$ |
$[0, 0, 0, -475, 3750]$ |
\(y^2=x^3-475x+3750\) |
1400.g4 |
1400a1 |
1400.g |
1400a |
$4$ |
$4$ |
\( 2^{3} \cdot 5^{2} \cdot 7 \) |
\( - 2^{8} \cdot 5^{6} \cdot 7 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.9 |
2B |
$1$ |
$1$ |
|
$1$ |
$256$ |
$0.109539$ |
$432/7$ |
$[0, 0, 0, 25, 250]$ |
\(y^2=x^3+25x+250\) |
1400.h1 |
1400e1 |
1400.h |
1400e |
$1$ |
$1$ |
\( 2^{3} \cdot 5^{2} \cdot 7 \) |
\( - 2^{4} \cdot 5^{4} \cdot 7^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$0.260599409$ |
$1$ |
|
$6$ |
$144$ |
$-0.061508$ |
$172800/343$ |
$[0, 0, 0, 25, 75]$ |
\(y^2=x^3+25x+75\) |
1400.i1 |
1400m1 |
1400.i |
1400m |
$1$ |
$1$ |
\( 2^{3} \cdot 5^{2} \cdot 7 \) |
\( - 2^{11} \cdot 5^{8} \cdot 7^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.2.0.1 |
|
$1.675433852$ |
$1$ |
|
$2$ |
$1440$ |
$0.882195$ |
$-10303010/49$ |
$[0, 1, 0, -4208, -106912]$ |
\(y^2=x^3+x^2-4208x-106912\) |
1400.j1 |
1400l1 |
1400.j |
1400l |
$1$ |
$1$ |
\( 2^{3} \cdot 5^{2} \cdot 7 \) |
\( - 2^{8} \cdot 5^{9} \cdot 7^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$0.946553385$ |
$1$ |
|
$4$ |
$960$ |
$0.834789$ |
$1024/343$ |
$[0, 1, 0, 167, 19963]$ |
\(y^2=x^3+x^2+167x+19963\) |
1400.k1 |
1400j1 |
1400.k |
1400j |
$1$ |
$1$ |
\( 2^{3} \cdot 5^{2} \cdot 7 \) |
\( - 2^{8} \cdot 5^{7} \cdot 7 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$0.247646181$ |
$1$ |
|
$4$ |
$384$ |
$0.243388$ |
$-1024/35$ |
$[0, 1, 0, -33, 563]$ |
\(y^2=x^3+x^2-33x+563\) |
1400.l1 |
1400d1 |
1400.l |
1400d |
$1$ |
$1$ |
\( 2^{3} \cdot 5^{2} \cdot 7 \) |
\( - 2^{4} \cdot 5^{8} \cdot 7^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$1200$ |
$0.802279$ |
$-6288640/16807$ |
$[0, -1, 0, -708, -16963]$ |
\(y^2=x^3-x^2-708x-16963\) |
1400.m1 |
1400c1 |
1400.m |
1400c |
$1$ |
$1$ |
\( 2^{3} \cdot 5^{2} \cdot 7 \) |
\( - 2^{4} \cdot 5^{10} \cdot 7 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$720$ |
$0.429152$ |
$-6400/7$ |
$[0, -1, 0, -208, 2037]$ |
\(y^2=x^3-x^2-208x+2037\) |
1400.n1 |
1400i1 |
1400.n |
1400i |
$1$ |
$1$ |
\( 2^{3} \cdot 5^{2} \cdot 7 \) |
\( - 2^{8} \cdot 5^{11} \cdot 7^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$5760$ |
$1.196188$ |
$-30211716096/1071875$ |
$[0, 0, 0, -10300, 414500]$ |
\(y^2=x^3-10300x+414500\) |