| 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 |
| 1215.a1 |
1215c1 |
1215.a |
1215c |
$1$ |
$1$ |
\( 3^{5} \cdot 5 \) |
\( - 3^{7} \cdot 5^{4} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$0.427743658$ |
$1$ |
|
$4$ |
$216$ |
$-0.133613$ |
$995328/625$ |
$1.20397$ |
$3.02726$ |
$[0, 0, 1, 27, -16]$ |
\(y^2+y=x^3+27x-16\) |
6.2.0.a.1 |
$[(4, 12)]$ |
| 1215.b1 |
1215j1 |
1215.b |
1215j |
$1$ |
$1$ |
\( 3^{5} \cdot 5 \) |
\( 3^{5} \cdot 5^{5} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$60$ |
$2$ |
$0$ |
$0.188181468$ |
$1$ |
|
$4$ |
$180$ |
$-0.122840$ |
$46314747/3125$ |
$0.96113$ |
$3.25858$ |
$[1, -1, 1, -47, -104]$ |
\(y^2+xy+y=x^3-x^2-47x-104\) |
60.2.0.a.1 |
$[(-4, 4)]$ |
| 1215.c1 |
1215i1 |
1215.c |
1215i |
$1$ |
$1$ |
\( 3^{5} \cdot 5 \) |
\( - 3^{5} \cdot 5^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$0.260570771$ |
$1$ |
|
$4$ |
$72$ |
$-0.592060$ |
$-2187/25$ |
$1.04391$ |
$2.28315$ |
$[1, -1, 1, -2, 4]$ |
\(y^2+xy+y=x^3-x^2-2x+4\) |
6.2.0.a.1 |
$[(2, 1)]$ |
| 1215.d1 |
1215e1 |
1215.d |
1215e |
$1$ |
$1$ |
\( 3^{5} \cdot 5 \) |
\( 3^{13} \cdot 5 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$60$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$324$ |
$0.103073$ |
$177147/5$ |
$1.13104$ |
$3.71231$ |
$[1, -1, 1, -137, -566]$ |
\(y^2+xy+y=x^3-x^2-137x-566\) |
60.2.0.a.1 |
$[]$ |
| 1215.e1 |
1215a2 |
1215.e |
1215a |
$2$ |
$3$ |
\( 3^{5} \cdot 5 \) |
\( - 3^{11} \cdot 5^{2} \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$6$ |
$16$ |
$0$ |
$1.518950105$ |
$1$ |
|
$6$ |
$540$ |
$0.495576$ |
$-7283146752/25$ |
$1.17573$ |
$4.89878$ |
$[0, 0, 1, -2268, 41573]$ |
\(y^2+y=x^3-2268x+41573\) |
3.8.0-3.a.1.2, 6.16.0-6.b.1.2 |
$[(31, 32)]$ |
| 1215.e2 |
1215a1 |
1215.e |
1215a |
$2$ |
$3$ |
\( 3^{5} \cdot 5 \) |
\( - 3^{5} \cdot 5^{6} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$6$ |
$16$ |
$0$ |
$0.506316701$ |
$1$ |
|
$4$ |
$180$ |
$-0.053730$ |
$-2654208/15625$ |
$1.17810$ |
$3.19580$ |
$[0, 0, 1, -18, 98]$ |
\(y^2+y=x^3-18x+98\) |
3.8.0-3.a.1.1, 6.16.0-6.b.1.1 |
$[(16, 62)]$ |
| 1215.f1 |
1215d1 |
1215.f |
1215d |
$2$ |
$3$ |
\( 3^{5} \cdot 5 \) |
\( - 3^{5} \cdot 5^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$6$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$180$ |
$-0.053730$ |
$-7283146752/25$ |
$1.17573$ |
$3.97070$ |
$[0, 0, 1, -252, -1540]$ |
\(y^2+y=x^3-252x-1540\) |
3.8.0-3.a.1.1, 6.16.0-6.b.1.1 |
$[]$ |
| 1215.f2 |
1215d2 |
1215.f |
1215d |
$2$ |
$3$ |
\( 3^{5} \cdot 5 \) |
\( - 3^{11} \cdot 5^{6} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$6$ |
$16$ |
$0$ |
$1$ |
$1$ |
|
$2$ |
$540$ |
$0.495576$ |
$-2654208/15625$ |
$1.17810$ |
$4.12388$ |
$[0, 0, 1, -162, -2653]$ |
\(y^2+y=x^3-162x-2653\) |
3.8.0-3.a.1.2, 6.16.0-6.b.1.2 |
$[]$ |
| 1215.g1 |
1215h1 |
1215.g |
1215h |
$1$ |
$1$ |
\( 3^{5} \cdot 5 \) |
\( 3^{11} \cdot 5^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$60$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$540$ |
$0.426466$ |
$46314747/3125$ |
$0.96113$ |
$4.18665$ |
$[1, -1, 0, -420, 3221]$ |
\(y^2+xy=x^3-x^2-420x+3221\) |
60.2.0.a.1 |
$[]$ |
| 1215.h1 |
1215b1 |
1215.h |
1215b |
$1$ |
$1$ |
\( 3^{5} \cdot 5 \) |
\( 3^{7} \cdot 5 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$60$ |
$2$ |
$0$ |
$0.770195244$ |
$1$ |
|
$2$ |
$108$ |
$-0.446233$ |
$177147/5$ |
$1.13104$ |
$2.78423$ |
$[1, -1, 0, -15, 26]$ |
\(y^2+xy=x^3-x^2-15x+26\) |
60.2.0.a.1 |
$[(2, 0)]$ |
| 1215.i1 |
1215g1 |
1215.i |
1215g |
$1$ |
$1$ |
\( 3^{5} \cdot 5 \) |
\( - 3^{11} \cdot 5^{2} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$216$ |
$-0.042754$ |
$-2187/25$ |
$1.04391$ |
$3.21122$ |
$[1, -1, 0, -15, -100]$ |
\(y^2+xy=x^3-x^2-15x-100\) |
6.2.0.a.1 |
$[]$ |
| 1215.j1 |
1215f1 |
1215.j |
1215f |
$1$ |
$1$ |
\( 3^{5} \cdot 5 \) |
\( - 3^{13} \cdot 5^{4} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
$6$ |
$2$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$648$ |
$0.415693$ |
$995328/625$ |
$1.20397$ |
$3.95534$ |
$[0, 0, 1, 243, 425]$ |
\(y^2+y=x^3+243x+425\) |
6.2.0.a.1 |
$[]$ |
