Atkin-Lehner |
2+ 5+ 7- 11- |
Signs for the Atkin-Lehner involutions |
Class |
61600r |
Isogeny class |
Conductor |
61600 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
-847000000 = -1 · 26 · 56 · 7 · 112 |
Discriminant |
Eigenvalues |
2+ 2 5+ 7- 11- -4 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,142,-1288] |
[a1,a2,a3,a4,a6] |
Generators |
[8862:57925:216] |
Generators of the group modulo torsion |
j |
314432/847 |
j-invariant |
L |
9.5322127410928 |
L(r)(E,1)/r! |
Ω |
0.81471777224112 |
Real period |
R |
5.8500090866294 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997847 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
61600bf1 123200bt2 2464k1 |
Quadratic twists by: -4 8 5 |