Atkin-Lehner |
3+ 7+ 11+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
122199c |
Isogeny class |
Conductor |
122199 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
6518016 |
Modular degree for the optimal curve |
Δ |
-7400570651961190011 = -1 · 32 · 73 · 113 · 239 |
Discriminant |
Eigenvalues |
-2 3+ 1 7+ 11+ -2 4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-9461870,-11200075780] |
[a1,a2,a3,a4,a6] |
j |
-52012073111552/4108797 |
j-invariant |
L |
0.68864078621313 |
L(r)(E,1)/r! |
Ω |
0.043040098107366 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
122199i1 |
Quadratic twists by: -23 |