Atkin-Lehner |
3+ 5+ 7+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
69825g |
Isogeny class |
Conductor |
69825 |
Conductor |
∏ cp |
120 |
Product of Tamagawa factors cp |
deg |
506880 |
Modular degree for the optimal curve |
Δ |
-20900790348046875 = -1 · 32 · 58 · 74 · 195 |
Discriminant |
Eigenvalues |
0 3+ 5+ 7+ -5 -4 -1 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-141283,21638343] |
[a1,a2,a3,a4,a6] |
Generators |
[-8601:-157951:27] [-23:-4988:1] |
Generators of the group modulo torsion |
j |
-8313508102144/557122275 |
j-invariant |
L |
6.8274553433291 |
L(r)(E,1)/r! |
Ω |
0.37707568400412 |
Real period |
R |
0.15088605181541 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
13965n1 69825bo1 |
Quadratic twists by: 5 -7 |