Atkin-Lehner |
2+ 3- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
69312bk |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
262656 |
Modular degree for the optimal curve |
Δ |
-208694022647808 = -1 · 212 · 3 · 198 |
Discriminant |
Eigenvalues |
2+ 3- -4 1 -2 1 2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-9145,-775321] |
[a1,a2,a3,a4,a6] |
j |
-1216/3 |
j-invariant |
L |
1.8199215606686 |
L(r)(E,1)/r! |
Ω |
0.22749019421421 |
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 |
69312h1 34656c1 69312z1 |
Quadratic twists by: -4 8 -19 |