Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696cf |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
709632 |
Modular degree for the optimal curve |
Δ |
-2646568486536967872 = -1 · 26 · 313 · 1110 |
Discriminant |
Eigenvalues |
2+ 3- 2 1 11- -2 -4 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,87846,77626582] |
[a1,a2,a3,a4,a6] |
Generators |
[-168446648723:6310532107521:865523177] |
Generators of the group modulo torsion |
j |
61952/2187 |
j-invariant |
L |
7.4003620393903 |
L(r)(E,1)/r! |
Ω |
0.19339271666655 |
Real period |
R |
19.132990546252 |
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 |
69696ch1 34848cd1 23232cc1 69696cg1 |
Quadratic twists by: -4 8 -3 -11 |