Atkin-Lehner |
3+ 7- 11+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
50127g |
Isogeny class |
Conductor |
50127 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
10386432 |
Modular degree for the optimal curve |
Δ |
-7240178932177862979 = -1 · 33 · 79 · 118 · 31 |
Discriminant |
Eigenvalues |
2 3+ -1 7- 11+ 1 -4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-640437366,-6238041300835] |
[a1,a2,a3,a4,a6] |
Generators |
[4961322806516876248446989325685070844635700460051299943566003814903871915028142940579143587416482:385826530885184056913336401047113336878453171114668457042757643795679459734197496894015396969634741:154669311699691458716238660337941449074304777797717662238551669940292843898395949357425580776] |
Generators of the group modulo torsion |
j |
-719898619458974392963072/179418383397 |
j-invariant |
L |
8.6763311458974 |
L(r)(E,1)/r! |
Ω |
0.015005497308513 |
Real period |
R |
144.55254243681 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
50127n1 |
Quadratic twists by: -7 |