| 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 |
| 27690.bg2 |
27690bc1 |
27690.bg |
27690bc |
$2$ |
$7$ |
\( 2 \cdot 3 \cdot 5 \cdot 13 \cdot 71 \) |
\( - 2^{21} \cdot 3^{7} \cdot 5^{7} \cdot 13 \cdot 71 \) |
$1$ |
$\Z/7\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$7$ |
7.48.0.1 |
7B.1.1 |
$775320$ |
$96$ |
$2$ |
$1.751933353$ |
$1$ |
|
$18$ |
$526848$ |
$2.104267$ |
$-3591362198523471528961/330727587840000000$ |
$1.04205$ |
$4.86669$ |
$[1, 0, 0, -319040, 74649600]$ |
\(y^2+xy=x^3-319040x+74649600\) |
7.48.0-7.a.1.2, 110760.2.0.?, 775320.96.2.? |
$[(0, 8640)]$ |
| 83070.j2 |
83070g1 |
83070.j |
83070g |
$2$ |
$7$ |
\( 2 \cdot 3^{2} \cdot 5 \cdot 13 \cdot 71 \) |
\( - 2^{21} \cdot 3^{13} \cdot 5^{7} \cdot 13 \cdot 71 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$7$ |
7.24.0.1 |
7B.6.1 |
$775320$ |
$96$ |
$2$ |
$1$ |
$1$ |
|
$0$ |
$4214784$ |
$2.653572$ |
$-3591362198523471528961/330727587840000000$ |
$1.04205$ |
$4.97660$ |
$[1, -1, 0, -2871360, -2015539200]$ |
\(y^2+xy=x^3-x^2-2871360x-2015539200\) |
7.24.0.a.1, 21.48.0-7.a.1.2, 110760.2.0.?, 258440.48.0.?, 775320.96.2.? |
$[]$ |
| 138450.d2 |
138450df1 |
138450.d |
138450df |
$2$ |
$7$ |
\( 2 \cdot 3 \cdot 5^{2} \cdot 13 \cdot 71 \) |
\( - 2^{21} \cdot 3^{7} \cdot 5^{13} \cdot 13 \cdot 71 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$7$ |
7.24.0.1 |
7B.6.1 |
$775320$ |
$96$ |
$2$ |
$8.813153050$ |
$1$ |
|
$0$ |
$12644352$ |
$2.908985$ |
$-3591362198523471528961/330727587840000000$ |
$1.04205$ |
$5.02076$ |
$[1, 1, 0, -7976000, 9331200000]$ |
\(y^2+xy=x^3+x^2-7976000x+9331200000\) |
7.24.0.a.1, 35.48.0-7.a.1.1, 110760.2.0.?, 155064.48.0.?, 775320.96.2.? |
$[(18205/4, 2626065/4)]$ |
| 221520.t2 |
221520bd1 |
221520.t |
221520bd |
$2$ |
$7$ |
\( 2^{4} \cdot 3 \cdot 5 \cdot 13 \cdot 71 \) |
\( - 2^{33} \cdot 3^{7} \cdot 5^{7} \cdot 13 \cdot 71 \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$7$ |
7.24.0.1 |
7B.6.1 |
$775320$ |
$96$ |
$2$ |
$11.06332861$ |
$1$ |
|
$0$ |
$12644352$ |
$2.797413$ |
$-3591362198523471528961/330727587840000000$ |
$1.04205$ |
$4.72026$ |
$[0, -1, 0, -5104640, -4777574400]$ |
\(y^2=x^3-x^2-5104640x-4777574400\) |
7.24.0.a.1, 28.48.0-7.a.1.1, 110760.2.0.?, 775320.96.2.? |
$[(630445/2, 500523575/2)]$ |
| 359970.bi2 |
359970bi1 |
359970.bi |
359970bi |
$2$ |
$7$ |
\( 2 \cdot 3 \cdot 5 \cdot 13^{2} \cdot 71 \) |
\( - 2^{21} \cdot 3^{7} \cdot 5^{7} \cdot 13^{7} \cdot 71 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$7$ |
7.24.0.1 |
7B.6.1 |
$775320$ |
$96$ |
$2$ |
$1$ |
$1$ |
|
$0$ |
$88510464$ |
$3.386742$ |
$-3591362198523471528961/330727587840000000$ |
$1.04205$ |
$5.09390$ |
$[1, 0, 1, -53917764, 164059088962]$ |
\(y^2+xy+y=x^3-53917764x+164059088962\) |
7.24.0.a.1, 91.48.0.?, 59640.48.0.?, 110760.2.0.?, 775320.96.2.? |
$[]$ |
| 415350.dq2 |
415350dq1 |
415350.dq |
415350dq |
$2$ |
$7$ |
\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 \cdot 71 \) |
\( - 2^{21} \cdot 3^{13} \cdot 5^{13} \cdot 13 \cdot 71 \) |
$0$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$7$ |
7.24.0.1 |
7B.6.1 |
$775320$ |
$96$ |
$2$ |
$1$ |
$1$ |
|
$0$ |
$101154816$ |
$3.458290$ |
$-3591362198523471528961/330727587840000000$ |
$1.04205$ |
$5.10392$ |
$[1, -1, 1, -71784005, -252014184003]$ |
\(y^2+xy+y=x^3-x^2-71784005x-252014184003\) |
7.24.0.a.1, 105.48.0.?, 51688.48.0.?, 110760.2.0.?, 775320.96.2.? |
$[]$ |
