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 |
936.a1 |
936d1 |
936.a |
936d |
$2$ |
$2$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{16} \cdot 13^{3} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$156$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$1920$ |
$1.085691$ |
$1909913257984/129730653$ |
$1.03790$ |
$5.50197$ |
$[0, 0, 0, -5862, -162295]$ |
\(y^2=x^3-5862x-162295\) |
2.3.0.a.1, 12.6.0.c.1, 26.6.0.b.1, 156.12.0.? |
$[ ]$ |
936.a2 |
936d2 |
936.a |
936d |
$2$ |
$2$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( - 2^{8} \cdot 3^{11} \cdot 13^{6} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$156$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$3840$ |
$1.432266$ |
$77366117936/1172914587$ |
$1.04122$ |
$5.91021$ |
$[0, 0, 0, 5073, -698110]$ |
\(y^2=x^3+5073x-698110\) |
2.3.0.a.1, 6.6.0.a.1, 52.6.0.c.1, 156.12.0.? |
$[ ]$ |
936.b1 |
936e3 |
936.b |
936e |
$4$ |
$4$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( 2^{10} \cdot 3^{7} \cdot 13 \) |
$1$ |
$\Z/4\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.7 |
2B |
$312$ |
$48$ |
$0$ |
$2.580993217$ |
$1$ |
|
$7$ |
$512$ |
$0.752432$ |
$62275269892/39$ |
$1.05219$ |
$5.60949$ |
$[0, 0, 0, -7491, 249550]$ |
\(y^2=x^3-7491x+249550\) |
2.3.0.a.1, 4.12.0-4.c.1.1, 24.24.0-24.z.1.8, 104.24.0.?, 156.24.0.?, $\ldots$ |
$[(54, 50)]$ |
936.b2 |
936e2 |
936.b |
936e |
$4$ |
$4$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( 2^{8} \cdot 3^{8} \cdot 13^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.1 |
2Cs |
$156$ |
$48$ |
$0$ |
$1.290496608$ |
$1$ |
|
$11$ |
$256$ |
$0.405858$ |
$61918288/1521$ |
$0.98715$ |
$4.39636$ |
$[0, 0, 0, -471, 3850]$ |
\(y^2=x^3-471x+3850\) |
2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.b.1.2, 52.24.0-52.b.1.3, 156.48.0.? |
$[(2, 54)]$ |
936.b3 |
936e1 |
936.b |
936e |
$4$ |
$4$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{10} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.12.0.6 |
2B |
$312$ |
$48$ |
$0$ |
$0.645248304$ |
$1$ |
|
$7$ |
$128$ |
$0.059284$ |
$2725888/1053$ |
$0.92420$ |
$3.53463$ |
$[0, 0, 0, -66, -119]$ |
\(y^2=x^3-66x-119\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.2, 24.24.0-24.z.1.4, $\ldots$ |
$[(-4, 9)]$ |
936.b4 |
936e4 |
936.b |
936e |
$4$ |
$4$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( - 2^{10} \cdot 3^{7} \cdot 13^{4} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.12.0.8 |
2B |
$312$ |
$48$ |
$0$ |
$0.645248304$ |
$1$ |
|
$7$ |
$512$ |
$0.752432$ |
$48668/85683$ |
$1.07537$ |
$4.72636$ |
$[0, 0, 0, 69, 12166]$ |
\(y^2=x^3+69x+12166\) |
2.3.0.a.1, 4.12.0-4.c.1.2, 6.6.0.a.1, 12.24.0-12.g.1.1, 104.24.0.?, $\ldots$ |
$[(-9, 104)]$ |
936.c1 |
936a2 |
936.c |
936a |
$2$ |
$2$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( 2^{10} \cdot 3^{3} \cdot 13^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$156$ |
$12$ |
$0$ |
$0.502278946$ |
$1$ |
|
$7$ |
$128$ |
$-0.016441$ |
$530604/169$ |
$0.85497$ |
$3.42157$ |
$[0, 0, 0, -51, 94]$ |
\(y^2=x^3-51x+94\) |
2.3.0.a.1, 12.6.0.a.1, 52.6.0.e.1, 156.12.0.? |
$[(-1, 12)]$ |
936.c2 |
936a1 |
936.c |
936a |
$2$ |
$2$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( - 2^{8} \cdot 3^{3} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$156$ |
$12$ |
$0$ |
$1.004557893$ |
$1$ |
|
$7$ |
$64$ |
$-0.363015$ |
$11664/13$ |
$0.66228$ |
$2.66096$ |
$[0, 0, 0, 9, 10]$ |
\(y^2=x^3+9x+10\) |
2.3.0.a.1, 12.6.0.b.1, 52.6.0.e.1, 78.6.0.?, 156.12.0.? |
$[(2, 6)]$ |
936.d1 |
936h1 |
936.d |
936h |
$2$ |
$2$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{8} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$156$ |
$12$ |
$0$ |
$0.471749473$ |
$1$ |
|
$7$ |
$128$ |
$-0.127868$ |
$256000/117$ |
$0.88864$ |
$3.18890$ |
$[0, 0, 0, -30, 29]$ |
\(y^2=x^3-30x+29\) |
2.3.0.a.1, 12.6.0.c.1, 26.6.0.b.1, 156.12.0.? |
$[(-2, 9)]$ |
936.d2 |
936h2 |
936.d |
936h |
$2$ |
$2$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( - 2^{8} \cdot 3^{7} \cdot 13^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$156$ |
$12$ |
$0$ |
$0.235874736$ |
$1$ |
|
$13$ |
$256$ |
$0.218706$ |
$686000/507$ |
$0.86569$ |
$3.73822$ |
$[0, 0, 0, 105, 218]$ |
\(y^2=x^3+105x+218\) |
2.3.0.a.1, 6.6.0.a.1, 52.6.0.c.1, 156.12.0.? |
$[(1, 18)]$ |
936.e1 |
936g2 |
936.e |
936g |
$2$ |
$2$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( 2^{8} \cdot 3^{8} \cdot 13 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$156$ |
$12$ |
$0$ |
$0.276483254$ |
$1$ |
|
$11$ |
$256$ |
$0.335445$ |
$137842000/117$ |
$0.90407$ |
$4.51333$ |
$[0, 0, 0, -615, 5866]$ |
\(y^2=x^3-615x+5866\) |
2.3.0.a.1, 12.6.0.c.1, 26.6.0.b.1, 156.12.0.? |
$[(5, 54)]$ |
936.e2 |
936g1 |
936.e |
936g |
$2$ |
$2$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( - 2^{4} \cdot 3^{7} \cdot 13^{2} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$156$ |
$12$ |
$0$ |
$0.552966508$ |
$1$ |
|
$9$ |
$128$ |
$-0.011129$ |
$-256000/507$ |
$0.90091$ |
$3.40619$ |
$[0, 0, 0, -30, 133]$ |
\(y^2=x^3-30x+133\) |
2.3.0.a.1, 6.6.0.a.1, 52.6.0.c.1, 156.12.0.? |
$[(2, 9)]$ |
936.f1 |
936b1 |
936.f |
936b |
$1$ |
$1$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( - 2^{11} \cdot 3^{6} \cdot 13 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$104$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$240$ |
$0.156275$ |
$-235298/13$ |
$0.96559$ |
$3.89909$ |
$[0, 0, 0, -147, 718]$ |
\(y^2=x^3-147x+718\) |
104.2.0.? |
$[ ]$ |
936.g1 |
936f2 |
936.g |
936f |
$2$ |
$2$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( 2^{10} \cdot 3^{9} \cdot 13^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$156$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$384$ |
$0.532865$ |
$530604/169$ |
$0.85497$ |
$4.38504$ |
$[0, 0, 0, -459, -2538]$ |
\(y^2=x^3-459x-2538\) |
2.3.0.a.1, 12.6.0.a.1, 52.6.0.e.1, 156.12.0.? |
$[ ]$ |
936.g2 |
936f1 |
936.g |
936f |
$2$ |
$2$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( - 2^{8} \cdot 3^{9} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$156$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$192$ |
$0.186291$ |
$11664/13$ |
$0.66228$ |
$3.62443$ |
$[0, 0, 0, 81, -270]$ |
\(y^2=x^3+81x-270\) |
2.3.0.a.1, 12.6.0.b.1, 52.6.0.e.1, 78.6.0.?, 156.12.0.? |
$[ ]$ |
936.h1 |
936i3 |
936.h |
936i |
$4$ |
$4$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( 2^{10} \cdot 3^{14} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.16 |
2B |
$624$ |
$192$ |
$3$ |
$1$ |
$1$ |
|
$1$ |
$1024$ |
$0.852139$ |
$3044193988/85293$ |
$0.95679$ |
$5.16832$ |
$[0, 0, 0, -2739, 53822]$ |
\(y^2=x^3-2739x+53822\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 12.12.0-4.c.1.1, 16.24.0-8.o.1.4, $\ldots$ |
$[ ]$ |
936.h2 |
936i2 |
936.h |
936i |
$4$ |
$4$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( 2^{8} \cdot 3^{10} \cdot 13^{2} \) |
$0$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
8.24.0.33 |
2Cs |
$312$ |
$192$ |
$3$ |
$1$ |
$1$ |
|
$3$ |
$512$ |
$0.505566$ |
$37642192/13689$ |
$0.91195$ |
$4.32361$ |
$[0, 0, 0, -399, -1870]$ |
\(y^2=x^3-399x-1870\) |
2.6.0.a.1, 4.12.0.a.1, 8.24.0-4.a.1.3, 12.24.0-4.a.1.1, 24.48.0-24.k.1.2, $\ldots$ |
$[ ]$ |
936.h3 |
936i1 |
936.h |
936i |
$4$ |
$4$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( 2^{4} \cdot 3^{8} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
16.24.0.16 |
2B |
$624$ |
$192$ |
$3$ |
$1$ |
$1$ |
|
$1$ |
$256$ |
$0.158993$ |
$420616192/117$ |
$0.96408$ |
$4.27114$ |
$[0, 0, 0, -354, -2563]$ |
\(y^2=x^3-354x-2563\) |
2.3.0.a.1, 4.6.0.c.1, 8.12.0.o.1, 12.12.0-4.c.1.2, 16.24.0-8.o.1.4, $\ldots$ |
$[ ]$ |
936.h4 |
936i4 |
936.h |
936i |
$4$ |
$4$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( - 2^{10} \cdot 3^{8} \cdot 13^{4} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.24.0.9 |
2B |
$624$ |
$192$ |
$3$ |
$1$ |
$1$ |
|
$1$ |
$1024$ |
$0.852139$ |
$269676572/257049$ |
$0.96683$ |
$4.81405$ |
$[0, 0, 0, 1221, -13210]$ |
\(y^2=x^3+1221x-13210\) |
2.3.0.a.1, 4.24.0-4.d.1.2, 12.48.0-12.e.1.1, 104.48.0.?, 208.96.0.?, $\ldots$ |
$[ ]$ |
936.i1 |
936c2 |
936.i |
936c |
$2$ |
$2$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( 2^{8} \cdot 3^{12} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$156$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$768$ |
$0.510839$ |
$94875856/9477$ |
$0.90366$ |
$4.45873$ |
$[0, 0, 0, -543, -4430]$ |
\(y^2=x^3-543x-4430\) |
2.3.0.a.1, 12.6.0.c.1, 26.6.0.b.1, 156.12.0.? |
$[ ]$ |
936.i2 |
936c1 |
936.i |
936c |
$2$ |
$2$ |
\( 2^{3} \cdot 3^{2} \cdot 13 \) |
\( - 2^{4} \cdot 3^{9} \cdot 13^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.3.0.1 |
2B |
$156$ |
$12$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$384$ |
$0.164265$ |
$702464/4563$ |
$0.96739$ |
$3.67624$ |
$[0, 0, 0, 42, -335]$ |
\(y^2=x^3+42x-335\) |
2.3.0.a.1, 6.6.0.a.1, 52.6.0.c.1, 156.12.0.? |
$[ ]$ |