Atkin-Lehner |
2+ 3+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312t |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
4147200 |
Modular degree for the optimal curve |
Δ |
6.6340510027033E+21 |
Discriminant |
Eigenvalues |
2+ 3+ -2 0 4 2 -6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-8133089,8024196705] |
[a1,a2,a3,a4,a6] |
j |
4824238966273/537919488 |
j-invariant |
L |
0.25830759175397 |
L(r)(E,1)/r! |
Ω |
0.12915379755008 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69312do1 2166d1 3648r1 |
Quadratic twists by: -4 8 -19 |