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 |
Weierstrass coefficients |
Weierstrass equation |
mod-$m$ images |
MW-generators |
816.a1 |
816c1 |
816.a |
816c |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( - 2^{8} \cdot 3^{5} \cdot 17 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$102$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$160$ |
$-0.154003$ |
$-2249728/4131$ |
$[0, -1, 0, -17, -51]$ |
\(y^2=x^3-x^2-17x-51\) |
102.2.0.? |
$[]$ |
816.b1 |
816h5 |
816.b |
816h |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( 2^{13} \cdot 3^{2} \cdot 17^{2} \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.96.0.94 |
2B |
$272$ |
$192$ |
$1$ |
$1.913490884$ |
$1$ |
|
$7$ |
$3072$ |
$1.540226$ |
$2361739090258884097/5202$ |
$[0, -1, 0, -443904, 113984640]$ |
\(y^2=x^3-x^2-443904x+113984640\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.48.0-8.r.1.2, 16.96.0-16.l.2.4, 136.96.0.?, $\ldots$ |
$[(360, 840)]$ |
816.b2 |
816h3 |
816.b |
816h |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( 2^{14} \cdot 3^{4} \cdot 17^{4} \) |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.96.0.35 |
2Cs |
$136$ |
$192$ |
$1$ |
$3.826981769$ |
$1$ |
|
$11$ |
$1536$ |
$1.193651$ |
$576615941610337/27060804$ |
$[0, -1, 0, -27744, 1787904]$ |
\(y^2=x^3-x^2-27744x+1787904\) |
2.6.0.a.1, 4.24.0-4.b.1.3, 8.96.0-8.e.1.5, 136.192.1.? |
$[(146, 910)]$ |
816.b3 |
816h6 |
816.b |
816h |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( - 2^{13} \cdot 3^{2} \cdot 17^{8} \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.96.0.156 |
2B |
$272$ |
$192$ |
$1$ |
$1.913490884$ |
$1$ |
|
$9$ |
$3072$ |
$1.540226$ |
$-491411892194497/125563633938$ |
$[0, -1, 0, -26304, 1980288]$ |
\(y^2=x^3-x^2-26304x+1980288\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.96.0-8.m.2.2, 272.192.1.? |
$[(81, 612)]$ |
816.b4 |
816h2 |
816.b |
816h |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( 2^{16} \cdot 3^{8} \cdot 17^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.96.0.55 |
2Cs |
$136$ |
$192$ |
$1$ |
$1.913490884$ |
$1$ |
|
$9$ |
$768$ |
$0.847078$ |
$163936758817/30338064$ |
$[0, -1, 0, -1824, 25344]$ |
\(y^2=x^3-x^2-1824x+25344\) |
2.6.0.a.1, 4.24.0-4.b.1.1, 8.96.0-8.h.2.4, 68.48.0-68.c.1.2, 136.192.1.? |
$[(50, 238)]$ |
816.b5 |
816h1 |
816.b |
816h |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( 2^{20} \cdot 3^{4} \cdot 17 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.96.0.145 |
2B |
$272$ |
$192$ |
$1$ |
$0.956745442$ |
$1$ |
|
$7$ |
$384$ |
$0.500504$ |
$4354703137/352512$ |
$[0, -1, 0, -544, -4352]$ |
\(y^2=x^3-x^2-544x-4352\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.bb.1.3, 16.96.0-16.bb.1.3, 34.6.0.a.1, $\ldots$ |
$[(-14, 18)]$ |
816.b6 |
816h4 |
816.b |
816h |
$6$ |
$8$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( - 2^{14} \cdot 3^{16} \cdot 17 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.96.0.151 |
2B |
$272$ |
$192$ |
$1$ |
$3.826981769$ |
$1$ |
|
$3$ |
$1536$ |
$1.193651$ |
$1276229915423/2927177028$ |
$[0, -1, 0, 3616, 142848]$ |
\(y^2=x^3-x^2+3616x+142848\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.48.0-8.ba.2.6, 16.96.0-16.y.2.6, 68.24.0-68.h.1.1, $\ldots$ |
$[(18, 462)]$ |
816.c1 |
816a1 |
816.c |
816a |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( 2^{10} \cdot 3^{2} \cdot 17 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.4 |
2B |
$136$ |
$12$ |
$0$ |
$0.304718385$ |
$1$ |
|
$11$ |
$64$ |
$-0.193734$ |
$12194500/153$ |
$[0, -1, 0, -48, 144]$ |
\(y^2=x^3-x^2-48x+144\) |
2.3.0.a.1, 8.6.0.d.1, 34.6.0.a.1, 136.12.0.? |
$[(6, 6)]$ |
816.c2 |
816a2 |
816.c |
816a |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( - 2^{11} \cdot 3^{4} \cdot 17^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.5 |
2B |
$136$ |
$12$ |
$0$ |
$0.609436770$ |
$1$ |
|
$7$ |
$128$ |
$0.152840$ |
$-31250/23409$ |
$[0, -1, 0, -8, 336]$ |
\(y^2=x^3-x^2-8x+336\) |
2.3.0.a.1, 8.6.0.a.1, 68.6.0.c.1, 136.12.0.? |
$[(2, 18)]$ |
816.d1 |
816e3 |
816.d |
816e |
$4$ |
$6$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( 2^{30} \cdot 3^{2} \cdot 17^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.4, 3.4.0.1 |
2B, 3B |
$408$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$1728$ |
$1.334574$ |
$46753267515625/11591221248$ |
$[0, -1, 0, -12008, 386928]$ |
\(y^2=x^3-x^2-12008x+386928\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.d.1, 12.24.0-6.a.1.9, $\ldots$ |
$[]$ |
816.d2 |
816e1 |
816.d |
816e |
$4$ |
$6$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( 2^{18} \cdot 3^{6} \cdot 17 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.4, 3.4.0.1 |
2B, 3B |
$408$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$576$ |
$0.785268$ |
$1845026709625/793152$ |
$[0, -1, 0, -4088, -99216]$ |
\(y^2=x^3-x^2-4088x-99216\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.d.1, 12.24.0-6.a.1.3, $\ldots$ |
$[]$ |
816.d3 |
816e2 |
816.d |
816e |
$4$ |
$6$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( - 2^{15} \cdot 3^{12} \cdot 17^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.5, 3.4.0.1 |
2B, 3B |
$408$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$1152$ |
$1.131842$ |
$-1107111813625/1228691592$ |
$[0, -1, 0, -3448, -131984]$ |
\(y^2=x^3-x^2-3448x-131984\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.a.1, 12.24.0-6.a.1.3, $\ldots$ |
$[]$ |
816.d4 |
816e4 |
816.d |
816e |
$4$ |
$6$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( - 2^{21} \cdot 3^{4} \cdot 17^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.5, 3.4.0.1 |
2B, 3B |
$408$ |
$96$ |
$1$ |
$1$ |
$1$ |
|
$1$ |
$3456$ |
$1.681147$ |
$655215969476375/1001033261568$ |
$[0, -1, 0, 28952, 2418544]$ |
\(y^2=x^3-x^2+28952x+2418544\) |
2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 8.6.0.a.1, 12.24.0-6.a.1.9, $\ldots$ |
$[]$ |
816.e1 |
816g1 |
816.e |
816g |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( - 2^{8} \cdot 3 \cdot 17 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$102$ |
$2$ |
$0$ |
$0.282674944$ |
$1$ |
|
$6$ |
$48$ |
$-0.511542$ |
$-65536/51$ |
$[0, -1, 0, -5, 9]$ |
\(y^2=x^3-x^2-5x+9\) |
102.2.0.? |
$[(1, 2)]$ |
816.f1 |
816b3 |
816.f |
816b |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( 2^{11} \cdot 3^{8} \cdot 17 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.104 |
2B |
$136$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$512$ |
$0.452304$ |
$22994537186/111537$ |
$[0, -1, 0, -752, 8160]$ |
\(y^2=x^3-x^2-752x+8160\) |
2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.m.1.7, 68.12.0-4.c.1.2, 136.48.0.? |
$[]$ |
816.f2 |
816b2 |
816.f |
816b |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( 2^{10} \cdot 3^{4} \cdot 17^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.3 |
2Cs |
$136$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$256$ |
$0.105731$ |
$40873252/23409$ |
$[0, -1, 0, -72, 0]$ |
\(y^2=x^3-x^2-72x\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.b.1.1, 68.24.0-68.b.1.2, 136.48.0.? |
$[]$ |
816.f3 |
816b1 |
816.f |
816b |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( 2^{8} \cdot 3^{2} \cdot 17 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.63 |
2B |
$136$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$128$ |
$-0.240843$ |
$61918288/153$ |
$[0, -1, 0, -52, -128]$ |
\(y^2=x^3-x^2-52x-128\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.m.1.3, 34.6.0.a.1, 68.24.0-68.g.1.1, $\ldots$ |
$[]$ |
816.f4 |
816b4 |
816.f |
816b |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( - 2^{11} \cdot 3^{2} \cdot 17^{4} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.48 |
2B |
$136$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$3$ |
$512$ |
$0.452304$ |
$1285471294/751689$ |
$[0, -1, 0, 288, -288]$ |
\(y^2=x^3-x^2+288x-288\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.d.1.2, 136.48.0.? |
$[]$ |
816.g1 |
816f2 |
816.g |
816f |
$2$ |
$3$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( - 2^{12} \cdot 3 \cdot 17^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$204$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$432$ |
$0.433924$ |
$-23100424192/14739$ |
$[0, -1, 0, -949, 11581]$ |
\(y^2=x^3-x^2-949x+11581\) |
3.4.0.a.1, 12.8.0-3.a.1.2, 102.8.0.?, 204.16.0.? |
$[]$ |
816.g2 |
816f1 |
816.g |
816f |
$2$ |
$3$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( - 2^{12} \cdot 3^{3} \cdot 17 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$204$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$144$ |
$-0.115383$ |
$32768/459$ |
$[0, -1, 0, 11, 61]$ |
\(y^2=x^3-x^2+11x+61\) |
3.4.0.a.1, 12.8.0-3.a.1.1, 102.8.0.?, 204.16.0.? |
$[]$ |
816.h1 |
816j1 |
816.h |
816j |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( 2^{14} \cdot 3^{2} \cdot 17 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.4 |
2B |
$136$ |
$12$ |
$0$ |
$0.592146060$ |
$1$ |
|
$7$ |
$192$ |
$-0.070381$ |
$1771561/612$ |
$[0, 1, 0, -40, -76]$ |
\(y^2=x^3+x^2-40x-76\) |
2.3.0.a.1, 8.6.0.d.1, 34.6.0.a.1, 136.12.0.? |
$[(-4, 6)]$ |
816.h2 |
816j2 |
816.h |
816j |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( - 2^{13} \cdot 3^{4} \cdot 17^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.5 |
2B |
$136$ |
$12$ |
$0$ |
$0.296073030$ |
$1$ |
|
$11$ |
$384$ |
$0.276193$ |
$46268279/46818$ |
$[0, 1, 0, 120, -396]$ |
\(y^2=x^3+x^2+120x-396\) |
2.3.0.a.1, 8.6.0.a.1, 68.6.0.c.1, 136.12.0.? |
$[(6, 24)]$ |
816.i1 |
816i1 |
816.i |
816i |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( - 2^{8} \cdot 3^{11} \cdot 17 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$102$ |
$2$ |
$0$ |
$0.067746189$ |
$1$ |
|
$10$ |
$528$ |
$0.601901$ |
$-1841198792704/3011499$ |
$[0, 1, 0, -1621, 24623]$ |
\(y^2=x^3+x^2-1621x+24623\) |
102.2.0.? |
$[(-1, 162)]$ |
816.j1 |
816d1 |
816.j |
816d |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 17 \) |
\( - 2^{8} \cdot 3^{3} \cdot 17^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$102$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$480$ |
$0.606012$ |
$57530252288/38336139$ |
$[0, 1, 0, 511, 1899]$ |
\(y^2=x^3+x^2+511x+1899\) |
102.2.0.? |
$[]$ |