Atkin-Lehner |
3+ 5- 11+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
68475b |
Isogeny class |
Conductor |
68475 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
23712 |
Modular degree for the optimal curve |
Δ |
-1562941875 = -1 · 3 · 54 · 112 · 832 |
Discriminant |
Eigenvalues |
0 3+ 5- -1 11+ -3 -4 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,67,1868] |
[a1,a2,a3,a4,a6] |
Generators |
[-8:27:1] [-2:41:1] |
Generators of the group modulo torsion |
j |
52428800/2500707 |
j-invariant |
L |
6.7522068459533 |
L(r)(E,1)/r! |
Ω |
1.1419246461002 |
Real period |
R |
0.49275046803517 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000047 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68475d1 |
Quadratic twists by: 5 |