Atkin-Lehner |
5+ 7- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
82075a |
Isogeny class |
Conductor |
82075 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
-3079094921875 = -1 · 58 · 76 · 67 |
Discriminant |
Eigenvalues |
0 0 5+ 7- -2 -2 -3 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-2450,-96469] |
[a1,a2,a3,a4,a6] |
Generators |
[65:137:1] [658:4063:8] |
Generators of the group modulo torsion |
j |
-884736/1675 |
j-invariant |
L |
8.3961190707622 |
L(r)(E,1)/r! |
Ω |
0.31946202922902 |
Real period |
R |
6.5705141006718 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000058 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16415b1 1675a1 |
Quadratic twists by: 5 -7 |