Atkin-Lehner |
2+ 7+ 19- 29- |
Signs for the Atkin-Lehner involutions |
Class |
30856b |
Isogeny class |
Conductor |
30856 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
73728 |
Modular degree for the optimal curve |
Δ |
-25739334656 = -1 · 210 · 74 · 192 · 29 |
Discriminant |
Eigenvalues |
2+ 1 -3 7+ -3 5 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-72392,7472864] |
[a1,a2,a3,a4,a6] |
Generators |
[164:196:1] |
Generators of the group modulo torsion |
j |
-40973350638896932/25136069 |
j-invariant |
L |
4.3781844262854 |
L(r)(E,1)/r! |
Ω |
0.98259777633637 |
Real period |
R |
0.55696549133889 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61712c1 |
Quadratic twists by: -4 |