| 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 |
| 2233.a2 |
2233a3 |
2233.a |
2233a |
$4$ |
$4$ |
\( 7 \cdot 11 \cdot 29 \) |
\( 7^{12} \cdot 11^{2} \cdot 29 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$2$ |
4.12.0.8 |
2B |
$1624$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$5376$ |
$1.387524$ |
$1048626554636928177/48569076788309$ |
$0.99097$ |
$5.38107$ |
$[1, -1, 1, -21166, -1131504]$ |
\(y^2+xy+y=x^3-x^2-21166x-1131504\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 56.24.0-56.z.1.12, 58.6.0.a.1, 116.24.0.?, $\ldots$ |
$[]$ |
| 15631.a2 |
15631c4 |
15631.a |
15631c |
$4$ |
$4$ |
\( 7^{2} \cdot 11 \cdot 29 \) |
\( 7^{18} \cdot 11^{2} \cdot 29 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.6 |
2B |
$1624$ |
$48$ |
$0$ |
$6.449693727$ |
$1$ |
|
$0$ |
$258048$ |
$2.360477$ |
$1048626554636928177/48569076788309$ |
$0.99097$ |
$5.50579$ |
$[1, -1, 1, -1037119, 390180018]$ |
\(y^2+xy+y=x^3-x^2-1037119x+390180018\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 28.12.0-4.c.1.1, 56.24.0-56.z.1.10, $\ldots$ |
$[(-657/2, 189303/2)]$ |
| 20097.l2 |
20097h4 |
20097.l |
20097h |
$4$ |
$4$ |
\( 3^{2} \cdot 7 \cdot 11 \cdot 29 \) |
\( 3^{6} \cdot 7^{12} \cdot 11^{2} \cdot 29 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$4872$ |
$48$ |
$0$ |
$9.672475586$ |
$1$ |
|
$0$ |
$172032$ |
$1.936829$ |
$1048626554636928177/48569076788309$ |
$0.99097$ |
$4.85306$ |
$[1, -1, 0, -190491, 30741092]$ |
\(y^2+xy=x^3-x^2-190491x+30741092\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 56.12.0.z.1, 58.6.0.a.1, $\ldots$ |
$[(52379/10, 8367297/10)]$ |
| 24563.g2 |
24563g3 |
24563.g |
24563g |
$4$ |
$4$ |
\( 7 \cdot 11^{2} \cdot 29 \) |
\( 7^{12} \cdot 11^{8} \cdot 29 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$17864$ |
$48$ |
$0$ |
$3.845160232$ |
$1$ |
|
$0$ |
$645120$ |
$2.586472$ |
$1048626554636928177/48569076788309$ |
$0.99097$ |
$5.52789$ |
$[1, -1, 0, -2561048, 1513714615]$ |
\(y^2+xy=x^3-x^2-2561048x+1513714615\) |
2.3.0.a.1, 4.6.0.c.1, 44.12.0-4.c.1.1, 56.12.0.z.1, 58.6.0.a.1, $\ldots$ |
$[(2919/2, 43043/2)]$ |
| 35728.m2 |
35728y3 |
35728.m |
35728y |
$4$ |
$4$ |
\( 2^{4} \cdot 7 \cdot 11 \cdot 29 \) |
\( 2^{12} \cdot 7^{12} \cdot 11^{2} \cdot 29 \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.7 |
2B |
$1624$ |
$48$ |
$0$ |
$2.802558060$ |
$1$ |
|
$7$ |
$344064$ |
$2.080669$ |
$1048626554636928177/48569076788309$ |
$0.99097$ |
$4.75136$ |
$[0, 0, 0, -338651, 72754890]$ |
\(y^2=x^3-338651x+72754890\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 56.24.0-56.z.1.4, 58.6.0.a.1, 116.24.0.?, $\ldots$ |
$[(278, 308)]$ |
| 55825.t2 |
55825l3 |
55825.t |
55825l |
$4$ |
$4$ |
\( 5^{2} \cdot 7 \cdot 11 \cdot 29 \) |
\( 5^{6} \cdot 7^{12} \cdot 11^{2} \cdot 29 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$8120$ |
$48$ |
$0$ |
$1.184374797$ |
$1$ |
|
$4$ |
$688128$ |
$2.192242$ |
$1048626554636928177/48569076788309$ |
$0.99097$ |
$4.67985$ |
$[1, -1, 0, -529142, -141967109]$ |
\(y^2+xy=x^3-x^2-529142x-141967109\) |
2.3.0.a.1, 4.6.0.c.1, 20.12.0-4.c.1.1, 56.12.0.z.1, 58.6.0.a.1, $\ldots$ |
$[(-426, 2663)]$ |
| 64757.h2 |
64757e3 |
64757.h |
64757e |
$4$ |
$4$ |
\( 7 \cdot 11 \cdot 29^{2} \) |
\( 7^{12} \cdot 11^{2} \cdot 29^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.8 |
2B |
$1624$ |
$48$ |
$0$ |
$1$ |
$9$ |
$3$ |
$0$ |
$4515840$ |
$3.071171$ |
$1048626554636928177/48569076788309$ |
$0.99097$ |
$5.56920$ |
$[1, -1, 0, -17800343, -27720846980]$ |
\(y^2+xy=x^3-x^2-17800343x-27720846980\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 56.24.0-56.z.1.5, 58.6.0.a.1, 116.24.0.?, $\ldots$ |
$[]$ |
| 140679.z2 |
140679y4 |
140679.z |
140679y |
$4$ |
$4$ |
\( 3^{2} \cdot 7^{2} \cdot 11 \cdot 29 \) |
\( 3^{6} \cdot 7^{18} \cdot 11^{2} \cdot 29 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$4872$ |
$48$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$8257536$ |
$2.909782$ |
$1048626554636928177/48569076788309$ |
$0.99097$ |
$5.04133$ |
$[1, -1, 0, -9334068, -10525526425]$ |
\(y^2+xy=x^3-x^2-9334068x-10525526425\) |
2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 56.12.0.z.1, 58.6.0.a.1, $\ldots$ |
$[]$ |
| 142912.bk2 |
142912bz4 |
142912.bk |
142912bz |
$4$ |
$4$ |
\( 2^{6} \cdot 7 \cdot 11 \cdot 29 \) |
\( 2^{18} \cdot 7^{12} \cdot 11^{2} \cdot 29 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.7 |
2B |
$1624$ |
$48$ |
$0$ |
$1$ |
$4$ |
$2$ |
$1$ |
$2752512$ |
$2.427242$ |
$1048626554636928177/48569076788309$ |
$0.99097$ |
$4.54682$ |
$[0, 0, 0, -1354604, -582039120]$ |
\(y^2=x^3-1354604x-582039120\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.3, 56.24.0-56.z.1.3, 58.6.0.a.1, $\ldots$ |
$[]$ |
| 142912.bm2 |
142912p3 |
142912.bm |
142912p |
$4$ |
$4$ |
\( 2^{6} \cdot 7 \cdot 11 \cdot 29 \) |
\( 2^{18} \cdot 7^{12} \cdot 11^{2} \cdot 29 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.8 |
2B |
$1624$ |
$48$ |
$0$ |
$2.267436200$ |
$1$ |
|
$5$ |
$2752512$ |
$2.427242$ |
$1048626554636928177/48569076788309$ |
$0.99097$ |
$4.54682$ |
$[0, 0, 0, -1354604, 582039120]$ |
\(y^2=x^3-1354604x+582039120\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.4, 56.24.0-56.z.1.11, 58.6.0.a.1, $\ldots$ |
$[(437, 8575)]$ |
| 171941.q2 |
171941q4 |
171941.q |
171941q |
$4$ |
$4$ |
\( 7^{2} \cdot 11^{2} \cdot 29 \) |
\( 7^{18} \cdot 11^{8} \cdot 29 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$17864$ |
$48$ |
$0$ |
$95.87699953$ |
$1$ |
|
$0$ |
$30965760$ |
$3.559425$ |
$1048626554636928177/48569076788309$ |
$0.99097$ |
$5.60410$ |
$[1, -1, 0, -125491361, -518953130228]$ |
\(y^2+xy=x^3-x^2-125491361x-518953130228\) |
2.3.0.a.1, 4.6.0.c.1, 56.12.0.z.1, 58.6.0.a.1, 88.12.0.?, $\ldots$ |
$[(4452309993678151110136801295811356644608331/7241829160907958470, 9292266265883632200535676359154438093377571782316997600763425719/7241829160907958470)]$ |
| 221067.l2 |
221067g4 |
221067.l |
221067g |
$4$ |
$4$ |
\( 3^{2} \cdot 7 \cdot 11^{2} \cdot 29 \) |
\( 3^{6} \cdot 7^{12} \cdot 11^{8} \cdot 29 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$53592$ |
$48$ |
$0$ |
$6.337508201$ |
$1$ |
|
$0$ |
$20643840$ |
$3.135777$ |
$1048626554636928177/48569076788309$ |
$0.99097$ |
$5.07654$ |
$[1, -1, 1, -23049434, -40847245172]$ |
\(y^2+xy+y=x^3-x^2-23049434x-40847245172\) |
2.3.0.a.1, 4.6.0.c.1, 56.12.0.z.1, 58.6.0.a.1, 116.12.0.?, $\ldots$ |
$[(-40451/4, 2354225/4)]$ |
| 250096.bl2 |
250096bl4 |
250096.bl |
250096bl |
$4$ |
$4$ |
\( 2^{4} \cdot 7^{2} \cdot 11 \cdot 29 \) |
\( 2^{12} \cdot 7^{18} \cdot 11^{2} \cdot 29 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.6 |
2B |
$1624$ |
$48$ |
$0$ |
$10.49174928$ |
$1$ |
|
$1$ |
$16515072$ |
$3.053623$ |
$1048626554636928177/48569076788309$ |
$0.99097$ |
$4.94684$ |
$[0, 0, 0, -16593899, -24954927270]$ |
\(y^2=x^3-16593899x-24954927270\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 28.12.0-4.c.1.2, 56.24.0-56.z.1.2, $\ldots$ |
$[(51055/3, 6801850/3)]$ |
| 321552.er2 |
321552er4 |
321552.er |
321552er |
$4$ |
$4$ |
\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 11 \cdot 29 \) |
\( 2^{12} \cdot 3^{6} \cdot 7^{12} \cdot 11^{2} \cdot 29 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$4872$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$11010048$ |
$2.629974$ |
$1048626554636928177/48569076788309$ |
$0.99097$ |
$4.44790$ |
$[0, 0, 0, -3047859, -1964382030]$ |
\(y^2=x^3-3047859x-1964382030\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 56.12.0.z.1, 58.6.0.a.1, $\ldots$ |
$[]$ |
| 377377.j2 |
377377j4 |
377377.j |
377377j |
$4$ |
$4$ |
\( 7 \cdot 11 \cdot 13^{2} \cdot 29 \) |
\( 7^{12} \cdot 11^{2} \cdot 13^{6} \cdot 29 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$21112$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$10321920$ |
$2.669998$ |
$1048626554636928177/48569076788309$ |
$0.99097$ |
$4.42985$ |
$[1, -1, 0, -3577001, -2496644708]$ |
\(y^2+xy=x^3-x^2-3577001x-2496644708\) |
2.3.0.a.1, 4.6.0.c.1, 52.12.0-4.c.1.1, 56.12.0.z.1, 58.6.0.a.1, $\ldots$ |
$[]$ |
| 390775.bm2 |
390775bm3 |
390775.bm |
390775bm |
$4$ |
$4$ |
\( 5^{2} \cdot 7^{2} \cdot 11 \cdot 29 \) |
\( 5^{6} \cdot 7^{18} \cdot 11^{2} \cdot 29 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$8120$ |
$48$ |
$0$ |
$11.75841076$ |
$1$ |
|
$0$ |
$33030144$ |
$3.165195$ |
$1048626554636928177/48569076788309$ |
$0.99097$ |
$4.87936$ |
$[1, -1, 0, -25927967, 48746574316]$ |
\(y^2+xy=x^3-x^2-25927967x+48746574316\) |
2.3.0.a.1, 4.6.0.c.1, 40.12.0-4.c.1.5, 56.12.0.z.1, 58.6.0.a.1, $\ldots$ |
$[(3565384/39, 1654841362/39)]$ |
| 393008.ba2 |
393008ba4 |
393008.ba |
393008ba |
$4$ |
$4$ |
\( 2^{4} \cdot 7 \cdot 11^{2} \cdot 29 \) |
\( 2^{12} \cdot 7^{12} \cdot 11^{8} \cdot 29 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$17864$ |
$48$ |
$0$ |
$9.383851259$ |
$1$ |
|
$1$ |
$41287680$ |
$3.279617$ |
$1048626554636928177/48569076788309$ |
$0.99097$ |
$4.98379$ |
$[0, 0, 0, -40976771, -96836758590]$ |
\(y^2=x^3-40976771x-96836758590\) |
2.3.0.a.1, 4.6.0.c.1, 44.12.0-4.c.1.2, 56.12.0.z.1, 58.6.0.a.1, $\ldots$ |
$[(228679/3, 105493850/3)]$ |
| 453299.q2 |
453299q3 |
453299.q |
453299q |
$4$ |
$4$ |
\( 7^{2} \cdot 11 \cdot 29^{2} \) |
\( 7^{18} \cdot 11^{2} \cdot 29^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.14 |
2B |
$1624$ |
$48$ |
$0$ |
$15.56142664$ |
$1$ |
|
$0$ |
$216760320$ |
$4.044128$ |
$1048626554636928177/48569076788309$ |
$0.99097$ |
$5.63356$ |
$[1, -1, 0, -872216816, 9509994947767]$ |
\(y^2+xy=x^3-x^2-872216816x+9509994947767\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.1, 28.12.0-4.c.1.1, 56.24.0-56.z.1.7, $\ldots$ |
$[(-21772119/64, 981410406773/64)]$ |
