Atkin-Lehner |
2- 3+ 19- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
12084a |
Isogeny class |
Conductor |
12084 |
Conductor |
∏ cp |
9 |
Product of Tamagawa factors cp |
deg |
19440 |
Modular degree for the optimal curve |
Δ |
114484831056 = 24 · 39 · 193 · 53 |
Discriminant |
Eigenvalues |
2- 3+ -1 3 2 -2 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-44441,3620802] |
[a1,a2,a3,a4,a6] |
Generators |
[121:19:1] |
Generators of the group modulo torsion |
j |
606687392623673344/7155301941 |
j-invariant |
L |
4.180863360242 |
L(r)(E,1)/r! |
Ω |
0.95536825340691 |
Real period |
R |
0.48624221257472 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
48336bj1 36252k1 |
Quadratic twists by: -4 -3 |