| 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 |
| 8464.a1 |
8464s1 |
8464.a |
8464s |
$1$ |
$1$ |
\( 2^{4} \cdot 23^{2} \) |
\( - 2^{19} \cdot 23^{4} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.2.0.1 |
|
$8$ |
$2$ |
$0$ |
$0.698964521$ |
$1$ |
|
$6$ |
$20160$ |
$1.049637$ |
$-97967097/128$ |
$1.09650$ |
$4.34144$ |
$[0, 0, 0, -10051, -388286]$ |
\(y^2=x^3-10051x-388286\) |
8.2.0.a.1 |
$[(161, 1472)]$ |
| 8464.b1 |
8464j1 |
8464.b |
8464j |
$1$ |
$1$ |
\( 2^{4} \cdot 23^{2} \) |
\( - 2^{4} \cdot 23^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$46$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$25344$ |
$1.180883$ |
$-1149984000/23$ |
$0.95837$ |
$4.69378$ |
$[0, 0, 0, -29095, -1910219]$ |
\(y^2=x^3-29095x-1910219\) |
46.2.0.a.1 |
$[]$ |
| 8464.c1 |
8464r1 |
8464.c |
8464r |
$1$ |
$1$ |
\( 2^{4} \cdot 23^{2} \) |
\( - 2^{19} \cdot 23^{10} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.2.0.1 |
|
$8$ |
$2$ |
$0$ |
$3.760702032$ |
$1$ |
|
$2$ |
$463680$ |
$2.617386$ |
$-97967097/128$ |
$1.09650$ |
$6.42170$ |
$[0, 0, 0, -5316979, 4724275762]$ |
\(y^2=x^3-5316979x+4724275762\) |
8.2.0.a.1 |
$[(1289, 3520)]$ |
| 8464.d1 |
8464i1 |
8464.d |
8464i |
$1$ |
$1$ |
\( 2^{4} \cdot 23^{2} \) |
\( - 2^{10} \cdot 23^{4} \) |
$2$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
4.4.0.3 |
|
$4$ |
$4$ |
$0$ |
$0.403731869$ |
$1$ |
|
$14$ |
$2688$ |
$0.328733$ |
$-2116$ |
$0.82141$ |
$3.06601$ |
$[0, 1, 0, -176, 1156]$ |
\(y^2=x^3+x^2-176x+1156\) |
4.4.0-4.a.1.1 |
$[(-8, 46), (37/2, 161/2)]$ |
| 8464.e1 |
8464h1 |
8464.e |
8464h |
$1$ |
$1$ |
\( 2^{4} \cdot 23^{2} \) |
\( - 2^{10} \cdot 23^{10} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2$ |
4.2.0.1 |
|
$92$ |
$4$ |
$0$ |
$1$ |
$4$ |
$2$ |
$0$ |
$61824$ |
$1.896481$ |
$-2116$ |
$0.82141$ |
$5.14627$ |
$[0, 1, 0, -93280, -14810844]$ |
\(y^2=x^3+x^2-93280x-14810844\) |
4.2.0.a.1, 92.4.0.? |
$[]$ |
| 8464.f1 |
8464n2 |
8464.f |
8464n |
$2$ |
$3$ |
\( 2^{4} \cdot 23^{2} \) |
\( - 2^{4} \cdot 23^{9} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$276$ |
$16$ |
$0$ |
$7.869802740$ |
$1$ |
|
$0$ |
$12672$ |
$1.297785$ |
$-42592000/12167$ |
$0.87185$ |
$4.37371$ |
$[0, -1, 0, -9698, -446045]$ |
\(y^2=x^3-x^2-9698x-446045\) |
3.4.0.a.1, 12.8.0-3.a.1.4, 46.2.0.a.1, 138.8.0.?, 276.16.0.? |
$[(59665/3, 14571305/3)]$ |
| 8464.f2 |
8464n1 |
8464.f |
8464n |
$2$ |
$3$ |
\( 2^{4} \cdot 23^{2} \) |
\( - 2^{4} \cdot 23^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$276$ |
$16$ |
$0$ |
$2.623267580$ |
$1$ |
|
$0$ |
$4224$ |
$0.748478$ |
$32000/23$ |
$0.71982$ |
$3.53389$ |
$[0, -1, 0, 882, 4663]$ |
\(y^2=x^3-x^2+882x+4663\) |
3.4.0.a.1, 12.8.0-3.a.1.3, 46.2.0.a.1, 138.8.0.?, 276.16.0.? |
$[(49/3, 2645/3)]$ |
| 8464.g1 |
8464m2 |
8464.g |
8464m |
$2$ |
$2$ |
\( 2^{4} \cdot 23^{2} \) |
\( 2^{17} \cdot 23^{8} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$184$ |
$12$ |
$0$ |
$8.202163631$ |
$1$ |
|
$1$ |
$126720$ |
$2.168987$ |
$545138290809/16928$ |
$1.08081$ |
$5.98823$ |
$[0, 0, 0, -1440467, -665413230]$ |
\(y^2=x^3-1440467x-665413230\) |
2.3.0.a.1, 8.6.0.b.1, 92.6.0.?, 184.12.0.? |
$[(721119/11, 598835406/11)]$ |
| 8464.g2 |
8464m1 |
8464.g |
8464m |
$2$ |
$2$ |
\( 2^{4} \cdot 23^{2} \) |
\( - 2^{22} \cdot 23^{7} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.1 |
2B |
$184$ |
$12$ |
$0$ |
$4.101081815$ |
$1$ |
|
$3$ |
$63360$ |
$1.822412$ |
$-116930169/23552$ |
$1.03422$ |
$5.08720$ |
$[0, 0, 0, -86227, -11315310]$ |
\(y^2=x^3-86227x-11315310\) |
2.3.0.a.1, 8.6.0.c.1, 46.6.0.a.1, 184.12.0.? |
$[(5911, 453882)]$ |
| 8464.h1 |
8464l1 |
8464.h |
8464l |
$1$ |
$1$ |
\( 2^{4} \cdot 23^{2} \) |
\( - 2^{8} \cdot 23^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 5$ |
4.2.0.1, 5.5.0.1 |
5S4 |
$920$ |
$20$ |
$0$ |
$3.591105759$ |
$1$ |
|
$0$ |
$576$ |
$-0.275208$ |
$-9936$ |
$0.66890$ |
$2.34204$ |
$[0, 0, 0, -23, -46]$ |
\(y^2=x^3-23x-46\) |
4.2.0.a.1, 5.5.0.a.1, 20.10.0.a.1, 184.4.0.?, 920.20.0.? |
$[(25/2, 59/2)]$ |
| 8464.i1 |
8464a2 |
8464.i |
8464a |
$2$ |
$2$ |
\( 2^{4} \cdot 23^{2} \) |
\( 2^{11} \cdot 23^{8} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.6 |
2B |
$184$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$25344$ |
$1.438200$ |
$2315250/529$ |
$0.89506$ |
$4.54384$ |
$[0, 0, 0, -18515, 754354]$ |
\(y^2=x^3-18515x+754354\) |
2.3.0.a.1, 8.6.0.b.1, 92.6.0.?, 184.12.0.? |
$[]$ |
| 8464.i2 |
8464a1 |
8464.i |
8464a |
$2$ |
$2$ |
\( 2^{4} \cdot 23^{2} \) |
\( - 2^{10} \cdot 23^{7} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.1 |
2B |
$184$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$12672$ |
$1.091627$ |
$13500/23$ |
$0.90383$ |
$3.97184$ |
$[0, 0, 0, 2645, 73002]$ |
\(y^2=x^3+2645x+73002\) |
2.3.0.a.1, 8.6.0.c.1, 46.6.0.a.1, 184.12.0.? |
$[]$ |
| 8464.j1 |
8464k1 |
8464.j |
8464k |
$1$ |
$1$ |
\( 2^{4} \cdot 23^{2} \) |
\( - 2^{8} \cdot 23^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 5$ |
8.4.0.2, 5.5.0.1 |
5S4 |
$40$ |
$20$ |
$0$ |
$2.149694905$ |
$1$ |
|
$0$ |
$13248$ |
$1.292540$ |
$-9936$ |
$0.66890$ |
$4.42230$ |
$[0, 0, 0, -12167, 559682]$ |
\(y^2=x^3-12167x+559682\) |
4.2.0.a.1, 5.5.0.a.1, 8.4.0-4.a.1.1, 20.10.0.a.1, 40.20.0-20.a.1.1 |
$[(529/2, 8993/2)]$ |
| 8464.k1 |
8464f1 |
8464.k |
8464f |
$1$ |
$1$ |
\( 2^{4} \cdot 23^{2} \) |
\( - 2^{11} \cdot 23^{8} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 5$ |
8.2.0.1, 5.5.0.1 |
5S4 |
$40$ |
$10$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$22080$ |
$1.406004$ |
$46$ |
$0.81518$ |
$4.43810$ |
$[0, 1, 0, 4056, -599788]$ |
\(y^2=x^3+x^2+4056x-599788\) |
5.5.0.a.1, 8.2.0.a.1, 40.10.0.a.1 |
$[]$ |
| 8464.l1 |
8464e1 |
8464.l |
8464e |
$1$ |
$1$ |
\( 2^{4} \cdot 23^{2} \) |
\( - 2^{4} \cdot 23^{9} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$46$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$17664$ |
$1.265408$ |
$256$ |
$0.66890$ |
$4.23355$ |
$[0, 1, 0, 4056, 239735]$ |
\(y^2=x^3+x^2+4056x+239735\) |
46.2.0.a.1 |
$[]$ |
| 8464.m1 |
8464d1 |
8464.m |
8464d |
$1$ |
$1$ |
\( 2^{4} \cdot 23^{2} \) |
\( - 2^{4} \cdot 23^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$46$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$8448$ |
$0.827628$ |
$-562432/23$ |
$0.75822$ |
$3.85841$ |
$[0, 1, 0, -2292, 42947]$ |
\(y^2=x^3+x^2-2292x+42947\) |
46.2.0.a.1 |
$[]$ |
| 8464.n1 |
8464c1 |
8464.n |
8464c |
$1$ |
$1$ |
\( 2^{4} \cdot 23^{2} \) |
\( - 2^{4} \cdot 23^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
|
|
|
$46$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$768$ |
$-0.302340$ |
$256$ |
$0.66890$ |
$2.15329$ |
$[0, 1, 0, 8, -17]$ |
\(y^2=x^3+x^2+8x-17\) |
46.2.0.a.1 |
$[]$ |
| 8464.o1 |
8464b1 |
8464.o |
8464b |
$1$ |
$1$ |
\( 2^{4} \cdot 23^{2} \) |
\( - 2^{11} \cdot 23^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
$2, 5$ |
8.2.0.1, 5.5.0.1 |
5S4 |
$40$ |
$10$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$960$ |
$-0.161744$ |
$46$ |
$0.81518$ |
$2.35784$ |
$[0, 1, 0, 8, 52]$ |
\(y^2=x^3+x^2+8x+52\) |
5.5.0.a.1, 8.2.0.a.1, 40.10.0.a.1 |
$[]$ |
| 8464.p1 |
8464g1 |
8464.p |
8464g |
$1$ |
$1$ |
\( 2^{4} \cdot 23^{2} \) |
\( - 2^{4} \cdot 23^{7} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$46$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$8448$ |
$0.739686$ |
$-256/23$ |
$0.98486$ |
$3.55857$ |
$[0, 1, 0, -176, 11207]$ |
\(y^2=x^3+x^2-176x+11207\) |
46.2.0.a.1 |
$[]$ |
| 8464.q1 |
8464p2 |
8464.q |
8464p |
$2$ |
$3$ |
\( 2^{4} \cdot 23^{2} \) |
\( - 2^{18} \cdot 23^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.2.0.1, 3.4.0.1 |
3B |
$276$ |
$32$ |
$0$ |
$7.535500269$ |
$1$ |
|
$2$ |
$5760$ |
$0.559827$ |
$-313994137/64$ |
$0.96923$ |
$3.77660$ |
$[0, -1, 0, -1832, -29584]$ |
\(y^2=x^3-x^2-1832x-29584\) |
3.4.0.a.1, 4.2.0.a.1, 12.16.0.b.2, 92.4.0.?, 138.8.0.?, $\ldots$ |
$[(1849, 79464)]$ |
| 8464.q2 |
8464p1 |
8464.q |
8464p |
$2$ |
$3$ |
\( 2^{4} \cdot 23^{2} \) |
\( - 2^{14} \cdot 23^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.2.0.1, 3.4.0.1 |
3B |
$276$ |
$32$ |
$0$ |
$2.511833423$ |
$1$ |
|
$2$ |
$1920$ |
$0.010521$ |
$23/4$ |
$0.94596$ |
$2.59039$ |
$[0, -1, 0, 8, -144]$ |
\(y^2=x^3-x^2+8x-144\) |
3.4.0.a.1, 4.2.0.a.1, 12.16.0.b.1, 92.4.0.?, 138.8.0.?, $\ldots$ |
$[(9, 24)]$ |
| 8464.r1 |
8464o2 |
8464.r |
8464o |
$2$ |
$3$ |
\( 2^{4} \cdot 23^{2} \) |
\( - 2^{18} \cdot 23^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.4.0.3, 3.4.0.1 |
3B |
$12$ |
$32$ |
$0$ |
$2.875274333$ |
$1$ |
|
$0$ |
$132480$ |
$2.127575$ |
$-313994137/64$ |
$0.96923$ |
$5.85686$ |
$[0, -1, 0, -969304, 367702512]$ |
\(y^2=x^3-x^2-969304x+367702512\) |
3.4.0.a.1, 4.4.0-4.a.1.1, 6.8.0-3.a.1.2, 12.32.0-12.b.2.2 |
$[(1941/2, 26979/2)]$ |
| 8464.r2 |
8464o1 |
8464.r |
8464o |
$2$ |
$3$ |
\( 2^{4} \cdot 23^{2} \) |
\( - 2^{14} \cdot 23^{8} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
4.4.0.3, 3.4.0.1 |
3B |
$12$ |
$32$ |
$0$ |
$8.625823001$ |
$1$ |
|
$0$ |
$44160$ |
$1.578268$ |
$23/4$ |
$0.94596$ |
$4.67065$ |
$[0, -1, 0, 4056, 1719152]$ |
\(y^2=x^3-x^2+4056x+1719152\) |
3.4.0.a.1, 4.4.0-4.a.1.1, 6.8.0-3.a.1.1, 12.32.0-12.b.1.2 |
$[(5261/2, 382041/2)]$ |
| 8464.s1 |
8464q1 |
8464.s |
8464q |
$1$ |
$1$ |
\( 2^{4} \cdot 23^{2} \) |
\( - 2^{4} \cdot 23^{7} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$46$ |
$2$ |
$0$ |
$1.823796260$ |
$1$ |
|
$0$ |
$12672$ |
$0.746334$ |
$-6912/23$ |
$0.66890$ |
$3.57559$ |
$[0, 0, 0, -529, 12167]$ |
\(y^2=x^3-529x+12167\) |
46.2.0.a.1 |
$[(46/3, 2645/3)]$ |
