Atkin-Lehner |
2+ 13+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
25688b |
Isogeny class |
Conductor |
25688 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
13440 |
Modular degree for the optimal curve |
Δ |
-19075549168 = -1 · 24 · 137 · 19 |
Discriminant |
Eigenvalues |
2+ 2 0 2 4 13+ -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1408,-20931] |
[a1,a2,a3,a4,a6] |
Generators |
[618:4563:8] |
Generators of the group modulo torsion |
j |
-4000000/247 |
j-invariant |
L |
8.6145409286114 |
L(r)(E,1)/r! |
Ω |
0.38827870431653 |
Real period |
R |
2.7733110369056 |
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 |
51376f1 1976b1 |
Quadratic twists by: -4 13 |