Atkin-Lehner |
2+ 3- 23- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
51336j |
Isogeny class |
Conductor |
51336 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
89088 |
Modular degree for the optimal curve |
Δ |
-1654362868464 = -1 · 24 · 38 · 232 · 313 |
Discriminant |
Eigenvalues |
2+ 3- -1 -1 0 4 2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-59763,5623711] |
[a1,a2,a3,a4,a6] |
Generators |
[131:207:1] |
Generators of the group modulo torsion |
j |
-2023826935542016/141834951 |
j-invariant |
L |
5.6813830998923 |
L(r)(E,1)/r! |
Ω |
0.80057024258278 |
Real period |
R |
0.88708379316684 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999959 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
102672g1 17112l1 |
Quadratic twists by: -4 -3 |