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 |
325.a1 |
325e2 |
325.a |
325e |
$2$ |
$5$ |
\( 5^{2} \cdot 13 \) |
\( 5^{10} \cdot 13 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.24.0.3 |
5B.1.2 |
$130$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$420$ |
$0.881910$ |
$23242854400/13$ |
$[0, -1, 1, -12708, -547182]$ |
\(y^2+y=x^3-x^2-12708x-547182\) |
5.24.0-5.a.2.2, 26.2.0.a.1, 130.48.1.? |
$[]$ |
325.a2 |
325e1 |
325.a |
325e |
$2$ |
$5$ |
\( 5^{2} \cdot 13 \) |
\( 5^{2} \cdot 13^{5} \) |
$0$ |
$\Z/5\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.24.0.1 |
5B.1.1 |
$130$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$4$ |
$84$ |
$0.077191$ |
$4206161920/371293$ |
$[0, -1, 1, -98, 378]$ |
\(y^2+y=x^3-x^2-98x+378\) |
5.24.0-5.a.1.2, 26.2.0.a.1, 130.48.1.? |
$[]$ |
325.b1 |
325b2 |
325.b |
325b |
$2$ |
$3$ |
\( 5^{2} \cdot 13 \) |
\( 5^{2} \cdot 13^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$390$ |
$16$ |
$0$ |
$0.771400805$ |
$1$ |
|
$4$ |
$36$ |
$-0.225118$ |
$671088640/2197$ |
$[0, -1, 1, -53, -132]$ |
\(y^2+y=x^3-x^2-53x-132\) |
3.4.0.a.1, 15.8.0-3.a.1.1, 26.2.0.a.1, 78.8.0.?, 390.16.0.? |
$[(-4, 0)]$ |
325.b2 |
325b1 |
325.b |
325b |
$2$ |
$3$ |
\( 5^{2} \cdot 13 \) |
\( 5^{2} \cdot 13 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.4.0.1 |
3B |
$390$ |
$16$ |
$0$ |
$0.257133601$ |
$1$ |
|
$4$ |
$12$ |
$-0.774425$ |
$163840/13$ |
$[0, -1, 1, -3, 3]$ |
\(y^2+y=x^3-x^2-3x+3\) |
3.4.0.a.1, 15.8.0-3.a.1.2, 26.2.0.a.1, 78.8.0.?, 390.16.0.? |
$[(1, 0)]$ |
325.c1 |
325a2 |
325.c |
325a |
$2$ |
$3$ |
\( 5^{2} \cdot 13 \) |
\( 5^{8} \cdot 13^{3} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.2 |
3B.1.2 |
$78$ |
$16$ |
$0$ |
$0.662972553$ |
$1$ |
|
$4$ |
$180$ |
$0.579600$ |
$671088640/2197$ |
$[0, 1, 1, -1333, -19131]$ |
\(y^2+y=x^3+x^2-1333x-19131\) |
3.8.0-3.a.1.1, 26.2.0.a.1, 78.16.0.? |
$[(-21, 6)]$ |
325.c2 |
325a1 |
325.c |
325a |
$2$ |
$3$ |
\( 5^{2} \cdot 13 \) |
\( 5^{8} \cdot 13 \) |
$1$ |
$\Z/3\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$3$ |
3.8.0.1 |
3B.1.1 |
$78$ |
$16$ |
$0$ |
$1.988917661$ |
$1$ |
|
$4$ |
$60$ |
$0.030295$ |
$163840/13$ |
$[0, 1, 1, -83, 244]$ |
\(y^2+y=x^3+x^2-83x+244\) |
3.8.0-3.a.1.2, 26.2.0.a.1, 78.16.0.? |
$[(2, 9)]$ |
325.d1 |
325c1 |
325.d |
325c |
$2$ |
$2$ |
\( 5^{2} \cdot 13 \) |
\( 5^{7} \cdot 13 \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.3 |
2B |
$520$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$1$ |
$48$ |
$-0.156896$ |
$117649/65$ |
$[1, 1, 0, -25, 0]$ |
\(y^2+xy=x^3+x^2-25x\) |
2.3.0.a.1, 4.6.0.b.1, 40.12.0-4.b.1.2, 104.12.0.?, 130.6.0.?, $\ldots$ |
$[]$ |
325.d2 |
325c2 |
325.d |
325c |
$2$ |
$2$ |
\( 5^{2} \cdot 13 \) |
\( - 5^{8} \cdot 13^{2} \) |
$0$ |
$\Z/2\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$2$ |
4.6.0.5 |
2B |
$520$ |
$48$ |
$0$ |
$1$ |
$1$ |
|
$0$ |
$96$ |
$0.189677$ |
$6967871/4225$ |
$[1, 1, 0, 100, 125]$ |
\(y^2+xy=x^3+x^2+100x+125\) |
2.3.0.a.1, 4.6.0.a.1, 40.12.0-4.a.1.1, 104.12.0.?, 260.12.0.?, $\ldots$ |
$[]$ |
325.e1 |
325d2 |
325.e |
325d |
$2$ |
$5$ |
\( 5^{2} \cdot 13 \) |
\( 5^{8} \cdot 13^{5} \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.24.0.2 |
5B.1.4 |
$130$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$420$ |
$0.881910$ |
$4206161920/371293$ |
$[0, 1, 1, -2458, 42369]$ |
\(y^2+y=x^3+x^2-2458x+42369\) |
5.24.0-5.a.1.1, 26.2.0.a.1, 130.48.1.? |
$[]$ |
325.e2 |
325d1 |
325.e |
325d |
$2$ |
$5$ |
\( 5^{2} \cdot 13 \) |
\( 5^{4} \cdot 13 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$5$ |
5.24.0.4 |
5B.1.3 |
$130$ |
$48$ |
$1$ |
$1$ |
$1$ |
|
$0$ |
$84$ |
$0.077191$ |
$23242854400/13$ |
$[0, 1, 1, -508, -4581]$ |
\(y^2+y=x^3+x^2-508x-4581\) |
5.24.0-5.a.2.1, 26.2.0.a.1, 130.48.1.? |
$[]$ |