Atkin-Lehner |
3+ 11- 73+ |
Signs for the Atkin-Lehner involutions |
Class |
2409c |
Isogeny class |
Conductor |
2409 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
14688 |
Modular degree for the optimal curve |
Δ |
-112106453406651 = -1 · 39 · 114 · 733 |
Discriminant |
Eigenvalues |
-2 3+ 1 -2 11- -2 7 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-56680,-5199966] |
[a1,a2,a3,a4,a6] |
j |
-20138211563024060416/112106453406651 |
j-invariant |
L |
0.61862419360543 |
L(r)(E,1)/r! |
Ω |
0.15465604840136 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
38544n1 7227d1 60225w1 118041n1 |
Quadratic twists by: -4 -3 5 -7 |