Atkin-Lehner |
2+ 7- 19- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
8246a |
Isogeny class |
Conductor |
8246 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
8320 |
Modular degree for the optimal curve |
Δ |
-574996086784 = -1 · 220 · 72 · 192 · 31 |
Discriminant |
Eigenvalues |
2+ 0 2 7- 2 -4 -4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-2156,-52528] |
[a1,a2,a3,a4,a6] |
Generators |
[3598:74011:8] |
Generators of the group modulo torsion |
j |
-1108621467544473/574996086784 |
j-invariant |
L |
3.4952548745633 |
L(r)(E,1)/r! |
Ω |
0.34195456468853 |
Real period |
R |
5.1107007121647 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
65968i1 74214w1 57722i1 |
Quadratic twists by: -4 -3 -7 |