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 |
912.a1 |
912a1 |
912.a |
912a |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( - 2^{8} \cdot 3^{6} \cdot 19 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$1.134807958$ |
$1$ |
|
$2$ |
$192$ |
$-0.016677$ |
$-81415168/13851$ |
$[0, -1, 0, -57, -171]$ |
\(y^2=x^3-x^2-57x-171\) |
912.b1 |
912g3 |
912.b |
912g |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( 2^{12} \cdot 3^{4} \cdot 19 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.8 |
2B |
$2.601893913$ |
$1$ |
|
$3$ |
$384$ |
$0.448139$ |
$115714886617/1539$ |
$[0, -1, 0, -1624, -24656]$ |
\(y^2=x^3-x^2-1624x-24656\) |
912.b2 |
912g2 |
912.b |
912g |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( 2^{12} \cdot 3^{2} \cdot 19^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.1 |
2Cs |
$1.300946956$ |
$1$ |
|
$9$ |
$192$ |
$0.101565$ |
$30664297/3249$ |
$[0, -1, 0, -104, -336]$ |
\(y^2=x^3-x^2-104x-336\) |
912.b3 |
912g1 |
912.b |
912g |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( 2^{12} \cdot 3 \cdot 19 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.6 |
2B |
$0.650473478$ |
$1$ |
|
$7$ |
$96$ |
$-0.245009$ |
$389017/57$ |
$[0, -1, 0, -24, 48]$ |
\(y^2=x^3-x^2-24x+48\) |
912.b4 |
912g4 |
912.b |
912g |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( - 2^{12} \cdot 3 \cdot 19^{4} \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.7 |
2B |
$2.601893913$ |
$1$ |
|
$7$ |
$384$ |
$0.448139$ |
$67419143/390963$ |
$[0, -1, 0, 136, -1872]$ |
\(y^2=x^3-x^2+136x-1872\) |
912.c1 |
912e3 |
912.c |
912e |
$4$ |
$6$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( 2^{14} \cdot 3 \cdot 19^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.4, 3.4.0.1 |
2B, 3B |
$1$ |
$1$ |
|
$1$ |
$864$ |
$0.798649$ |
$8671983378625/82308$ |
$[0, -1, 0, -6848, 220416]$ |
\(y^2=x^3-x^2-6848x+220416\) |
912.c2 |
912e4 |
912.c |
912e |
$4$ |
$6$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( - 2^{13} \cdot 3^{2} \cdot 19^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.5, 3.4.0.1 |
2B, 3B |
$1$ |
$1$ |
|
$1$ |
$1728$ |
$1.145224$ |
$-8078253774625/846825858$ |
$[0, -1, 0, -6688, 231040]$ |
\(y^2=x^3-x^2-6688x+231040\) |
912.c3 |
912e1 |
912.c |
912e |
$4$ |
$6$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( 2^{18} \cdot 3^{3} \cdot 19 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.4, 3.4.0.1 |
2B, 3B |
$1$ |
$1$ |
|
$1$ |
$288$ |
$0.249343$ |
$57066625/32832$ |
$[0, -1, 0, -128, 0]$ |
\(y^2=x^3-x^2-128x\) |
912.c4 |
912e2 |
912.c |
912e |
$4$ |
$6$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( - 2^{15} \cdot 3^{6} \cdot 19^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2, 3$ |
8.6.0.5, 3.4.0.1 |
2B, 3B |
$1$ |
$1$ |
|
$1$ |
$576$ |
$0.595917$ |
$3616805375/2105352$ |
$[0, -1, 0, 512, -512]$ |
\(y^2=x^3-x^2+512x-512\) |
912.d1 |
912f2 |
912.d |
912f |
$2$ |
$5$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( - 2^{12} \cdot 3^{2} \cdot 19^{5} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.12.0.2 |
5B.4.2 |
$0.226284916$ |
$1$ |
|
$4$ |
$2400$ |
$1.344555$ |
$-9358714467168256/22284891$ |
$[0, -1, 0, -70245, 7189389]$ |
\(y^2=x^3-x^2-70245x+7189389\) |
912.d2 |
912f1 |
912.d |
912f |
$2$ |
$5$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( - 2^{12} \cdot 3^{10} \cdot 19 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.12.0.1 |
5B.4.1 |
$1.131424581$ |
$1$ |
|
$2$ |
$480$ |
$0.539836$ |
$841232384/1121931$ |
$[0, -1, 0, 315, 2349]$ |
\(y^2=x^3-x^2+315x+2349\) |
912.e1 |
912b3 |
912.e |
912b |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( 2^{11} \cdot 3^{3} \cdot 19^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.7 |
2B |
$1$ |
$1$ |
|
$1$ |
$384$ |
$0.666203$ |
$111223479026/3518667$ |
$[0, -1, 0, -1272, -16560]$ |
\(y^2=x^3-x^2-1272x-16560\) |
912.e2 |
912b2 |
912.e |
912b |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( 2^{10} \cdot 3^{6} \cdot 19^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.1 |
2Cs |
$1$ |
$1$ |
|
$3$ |
$192$ |
$0.319629$ |
$768400132/263169$ |
$[0, -1, 0, -192, 720]$ |
\(y^2=x^3-x^2-192x+720\) |
912.e3 |
912b1 |
912.e |
912b |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( 2^{8} \cdot 3^{3} \cdot 19 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.12 |
2B |
$1$ |
$1$ |
|
$1$ |
$96$ |
$-0.026945$ |
$2211014608/513$ |
$[0, -1, 0, -172, 928]$ |
\(y^2=x^3-x^2-172x+928\) |
912.e4 |
912b4 |
912.e |
912b |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( - 2^{11} \cdot 3^{12} \cdot 19 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.8 |
2B |
$1$ |
$1$ |
|
$1$ |
$384$ |
$0.666203$ |
$9878111854/10097379$ |
$[0, -1, 0, 568, 4368]$ |
\(y^2=x^3-x^2+568x+4368\) |
912.f1 |
912i1 |
912.f |
912i |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( - 2^{8} \cdot 3^{2} \cdot 19 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$0.344049278$ |
$1$ |
|
$6$ |
$96$ |
$-0.429106$ |
$8192/171$ |
$[0, 1, 0, 3, -9]$ |
\(y^2=x^3+x^2+3x-9\) |
912.g1 |
912l1 |
912.g |
912l |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( - 2^{12} \cdot 3^{2} \cdot 19 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$160$ |
$-0.143401$ |
$-1404928/171$ |
$[0, 1, 0, -37, -109]$ |
\(y^2=x^3+x^2-37x-109\) |
912.h1 |
912h1 |
912.h |
912h |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( 2^{14} \cdot 3^{5} \cdot 19 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.4 |
2B |
$0.269535280$ |
$1$ |
|
$11$ |
$480$ |
$0.512457$ |
$96386901625/18468$ |
$[0, 1, 0, -1528, 22484]$ |
\(y^2=x^3+x^2-1528x+22484\) |
912.h2 |
912h2 |
912.h |
912h |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( - 2^{13} \cdot 3^{10} \cdot 19^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.5 |
2B |
$0.134767640$ |
$1$ |
|
$15$ |
$960$ |
$0.859030$ |
$-69173457625/42633378$ |
$[0, 1, 0, -1368, 27540]$ |
\(y^2=x^3+x^2-1368x+27540\) |
912.i1 |
912c1 |
912.i |
912c |
$1$ |
$1$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( - 2^{8} \cdot 3^{2} \cdot 19^{3} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$1$ |
$1$ |
|
$0$ |
$192$ |
$0.068805$ |
$70575104/61731$ |
$[0, 1, 0, 55, -93]$ |
\(y^2=x^3+x^2+55x-93\) |
912.j1 |
912j2 |
912.j |
912j |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( 2^{8} \cdot 3^{6} \cdot 19 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$1$ |
$1$ |
|
$1$ |
$144$ |
$0.022556$ |
$340062928/13851$ |
$[0, 1, 0, -92, -360]$ |
\(y^2=x^3+x^2-92x-360\) |
912.j2 |
912j1 |
912.j |
912j |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( - 2^{4} \cdot 3^{3} \cdot 19^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$1$ |
$1$ |
|
$1$ |
$72$ |
$-0.324018$ |
$131072/9747$ |
$[0, 1, 0, 3, -18]$ |
\(y^2=x^3+x^2+3x-18\) |
912.k1 |
912k3 |
912.k |
912k |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( 2^{17} \cdot 3^{3} \cdot 19 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.104 |
2B |
$1$ |
$1$ |
|
$1$ |
$5760$ |
$1.794586$ |
$74220219816682217473/16416$ |
$[0, 1, 0, -1400832, 637689780]$ |
\(y^2=x^3+x^2-1400832x+637689780\) |
912.k2 |
912k2 |
912.k |
912k |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( 2^{22} \cdot 3^{6} \cdot 19^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.3 |
2Cs |
$1$ |
$1$ |
|
$3$ |
$2880$ |
$1.448013$ |
$18120364883707393/269485056$ |
$[0, 1, 0, -87552, 9941940]$ |
\(y^2=x^3+x^2-87552x+9941940\) |
912.k3 |
912k4 |
912.k |
912k |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( - 2^{17} \cdot 3^{12} \cdot 19^{4} \) |
$0$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.48 |
2B |
$1$ |
$1$ |
|
$3$ |
$5760$ |
$1.794586$ |
$-16576888679672833/2216253521952$ |
$[0, 1, 0, -84992, 10553268]$ |
\(y^2=x^3+x^2-84992x+10553268\) |
912.k4 |
912k1 |
912.k |
912k |
$4$ |
$4$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( 2^{32} \cdot 3^{3} \cdot 19 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.63 |
2B |
$1$ |
$1$ |
|
$1$ |
$1440$ |
$1.101439$ |
$4824238966273/537919488$ |
$[0, 1, 0, -5632, 144308]$ |
\(y^2=x^3+x^2-5632x+144308\) |
912.l1 |
912d1 |
912.l |
912d |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( 2^{10} \cdot 3 \cdot 19 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.4 |
2B |
$1$ |
$1$ |
|
$1$ |
$160$ |
$-0.354923$ |
$470596/57$ |
$[0, 1, 0, -16, -28]$ |
\(y^2=x^3+x^2-16x-28\) |
912.l2 |
912d2 |
912.l |
912d |
$2$ |
$2$ |
\( 2^{4} \cdot 3 \cdot 19 \) |
\( - 2^{11} \cdot 3^{2} \cdot 19^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.6.0.5 |
2B |
$1$ |
$1$ |
|
$1$ |
$320$ |
$-0.008349$ |
$715822/3249$ |
$[0, 1, 0, 24, -108]$ |
\(y^2=x^3+x^2+24x-108\) |