Atkin-Lehner |
3- 5+ 7- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
58275r |
Isogeny class |
Conductor |
58275 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
589824 |
Modular degree for the optimal curve |
Δ |
-634976128025859375 = -1 · 322 · 57 · 7 · 37 |
Discriminant |
Eigenvalues |
-1 3- 5+ 7- 4 2 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-486005,-135806628] |
[a1,a2,a3,a4,a6] |
Generators |
[3129371130027296314:98206778765055428910:2195834106297833] |
Generators of the group modulo torsion |
j |
-1114544804970241/55745503695 |
j-invariant |
L |
4.6100000036478 |
L(r)(E,1)/r! |
Ω |
0.090145808454165 |
Real period |
R |
25.569685838234 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000075 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
19425f1 11655f1 |
Quadratic twists by: -3 5 |