| 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 |
Manin constant |
| 315.a1 |
315b3 |
315.a |
315b |
$4$ |
$4$ |
\( 3^{2} \cdot 5 \cdot 7 \) |
\( 3^{7} \cdot 5^{4} \cdot 7 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$840$ |
$48$ |
$0$ |
$0.259415011$ |
$1$ |
|
$10$ |
$128$ |
$0.383344$ |
$157551496201/13125$ |
$0.96087$ |
$5.62786$ |
$[1, -1, 1, -1013, 12656]$ |
\(y^2+xy+y=x^3-x^2-1013x+12656\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.1, 28.12.0-4.c.1.1, 40.12.0.ba.1, $\ldots$ |
$[(0, 112)]$ |
$1$ |
| 315.a2 |
315b2 |
315.a |
315b |
$4$ |
$4$ |
\( 3^{2} \cdot 5 \cdot 7 \) |
\( 3^{8} \cdot 5^{2} \cdot 7^{2} \) |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
2.6.0.1 |
2Cs |
$420$ |
$48$ |
$0$ |
$0.518830022$ |
$1$ |
|
$14$ |
$64$ |
$0.036770$ |
$47045881/11025$ |
$1.04751$ |
$4.21695$ |
$[1, -1, 1, -68, 182]$ |
\(y^2+xy+y=x^3-x^2-68x+182\) |
2.6.0.a.1, 12.12.0-2.a.1.1, 20.12.0.a.1, 28.12.0-2.a.1.1, 60.24.0-20.a.1.1, $\ldots$ |
$[(0, 13)]$ |
$1$ |
| 315.a3 |
315b1 |
315.a |
315b |
$4$ |
$4$ |
\( 3^{2} \cdot 5 \cdot 7 \) |
\( 3^{7} \cdot 5 \cdot 7 \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$840$ |
$48$ |
$0$ |
$1.037660045$ |
$1$ |
|
$7$ |
$32$ |
$-0.309803$ |
$1771561/105$ |
$0.96659$ |
$3.64690$ |
$[1, -1, 1, -23, -34]$ |
\(y^2+xy+y=x^3-x^2-23x-34\) |
2.3.0.a.1, 4.6.0.c.1, 24.12.0-4.c.1.3, 28.12.0-4.c.1.2, 40.12.0.ba.1, $\ldots$ |
$[(6, 1)]$ |
$1$ |
| 315.a4 |
315b4 |
315.a |
315b |
$4$ |
$4$ |
\( 3^{2} \cdot 5 \cdot 7 \) |
\( - 3^{10} \cdot 5 \cdot 7^{4} \) |
$1$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.1 |
2B |
$840$ |
$48$ |
$0$ |
$0.259415011$ |
$1$ |
|
$10$ |
$128$ |
$0.383344$ |
$590589719/972405$ |
$0.94478$ |
$4.76324$ |
$[1, -1, 1, 157, 992]$ |
\(y^2+xy+y=x^3-x^2+157x+992\) |
2.3.0.a.1, 4.6.0.c.1, 12.12.0-4.c.1.2, 20.12.0.h.1, 56.12.0-4.c.1.5, $\ldots$ |
$[(0, 31)]$ |
$1$ |
| 315.b1 |
315a3 |
315.b |
315a |
$3$ |
$9$ |
\( 3^{2} \cdot 5 \cdot 7 \) |
\( - 3^{6} \cdot 5^{9} \cdot 7 \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.24.0.1 |
3B.1.1 |
$630$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$180$ |
$0.676768$ |
$-250523582464/13671875$ |
$1.02112$ |
$5.72415$ |
$[0, 0, 1, -1182, 16362]$ |
\(y^2+y=x^3-1182x+16362\) |
3.8.0-3.a.1.2, 9.24.0-9.a.1.2, 63.72.0-63.e.2.4, 70.2.0.a.1, 210.16.0.?, $\ldots$ |
$[ ]$ |
$1$ |
| 315.b2 |
315a1 |
315.b |
315a |
$3$ |
$9$ |
\( 3^{2} \cdot 5 \cdot 7 \) |
\( - 3^{6} \cdot 5 \cdot 7 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
9.24.0.3 |
3B.1.2 |
$630$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$0$ |
$20$ |
$-0.421844$ |
$-262144/35$ |
$0.88715$ |
$3.35083$ |
$[0, 0, 1, -12, -18]$ |
\(y^2+y=x^3-12x-18\) |
3.8.0-3.a.1.1, 9.24.0-9.a.1.1, 63.72.0-63.e.1.1, 70.2.0.a.1, 210.16.0.?, $\ldots$ |
$[ ]$ |
$1$ |
| 315.b3 |
315a2 |
315.b |
315a |
$3$ |
$9$ |
\( 3^{2} \cdot 5 \cdot 7 \) |
\( - 3^{6} \cdot 5^{3} \cdot 7^{3} \) |
$0$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.24.0.1 |
3Cs.1.1 |
$630$ |
$144$ |
$3$ |
$1$ |
$1$ |
|
$2$ |
$60$ |
$0.127462$ |
$71991296/42875$ |
$1.06493$ |
$4.29090$ |
$[0, 0, 1, 78, 45]$ |
\(y^2+y=x^3+78x+45\) |
3.24.0-3.a.1.1, 63.72.0-63.b.1.1, 70.2.0.a.1, 210.48.1.?, 630.144.3.? |
$[ ]$ |
$1$ |
