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 |
42978.u1 |
42978r1 |
42978.u |
42978r |
$2$ |
$7$ |
\( 2 \cdot 3 \cdot 13 \cdot 19 \cdot 29 \) |
\( - 2^{28} \cdot 3^{7} \cdot 13 \cdot 19^{7} \cdot 29^{2} \) |
$1$ |
$\Z/7\Z$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
$7$ |
7.48.0.1 |
7B.1.1 |
$20748$ |
$96$ |
$2$ |
$2.575230045$ |
$1$ |
|
$16$ |
$11063808$ |
$3.700325$ |
$-10748395438529140294639078020769/5737242625602477531070464$ |
$1.01767$ |
$6.69762$ |
$[1, 0, 0, -459769306, 3796241996132]$ |
\(y^2+xy=x^3-459769306x+3796241996132\) |
7.48.0-7.a.1.2, 2964.2.0.?, 20748.96.2.? |
$[(9812, 474326)]$ |
128934.t1 |
128934i1 |
128934.t |
128934i |
$2$ |
$7$ |
\( 2 \cdot 3^{2} \cdot 13 \cdot 19 \cdot 29 \) |
\( - 2^{28} \cdot 3^{13} \cdot 13 \cdot 19^{7} \cdot 29^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$7$ |
7.24.0.1 |
7B.6.1 |
$20748$ |
$96$ |
$2$ |
$10.58591147$ |
$1$ |
|
$0$ |
$88510464$ |
$4.249634$ |
$-10748395438529140294639078020769/5737242625602477531070464$ |
$1.01767$ |
$6.63249$ |
$[1, -1, 0, -4137923754, -102498533895564]$ |
\(y^2+xy=x^3-x^2-4137923754x-102498533895564\) |
7.24.0.a.1, 21.48.0-7.a.1.2, 2964.2.0.?, 6916.48.0.?, 20748.96.2.? |
$[(10587631/10, 25368243591/10)]$ |
343824.j1 |
343824j1 |
343824.j |
343824j |
$2$ |
$7$ |
\( 2^{4} \cdot 3 \cdot 13 \cdot 19 \cdot 29 \) |
\( - 2^{40} \cdot 3^{7} \cdot 13 \cdot 19^{7} \cdot 29^{2} \) |
$1$ |
$\mathsf{trivial}$ |
$\Q$ |
|
$\mathrm{SU}(2)$ |
|
|
$7$ |
7.24.0.1 |
7B.6.1 |
$20748$ |
$96$ |
$2$ |
$144.6283318$ |
$1$ |
|
$0$ |
$265531392$ |
$4.393471$ |
$-10748395438529140294639078020769/5737242625602477531070464$ |
$1.01767$ |
$6.25759$ |
$[0, -1, 0, -7356308896, -242959487752448]$ |
\(y^2=x^3-x^2-7356308896x-242959487752448\) |
7.24.0.a.1, 28.48.0-7.a.1.1, 2964.2.0.?, 10374.48.0.?, 20748.96.2.? |
$[(931457204773888393995584835801461159372244512813837300931476922/85695159734617522181352185971, 18503718439595216690718851701812393742040889947537760917237535091039519561525081935479959419782/85695159734617522181352185971)]$ |