Atkin-Lehner |
2+ 3+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
69312a |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
262656 |
Modular degree for the optimal curve |
Δ |
-469561550957568 = -1 · 210 · 33 · 198 |
Discriminant |
Eigenvalues |
2+ 3+ 0 3 -2 -1 4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-91453,-10665491] |
[a1,a2,a3,a4,a6] |
Generators |
[2723691512355:197191096918516:517781627] |
Generators of the group modulo torsion |
j |
-4864000/27 |
j-invariant |
L |
5.8413244849481 |
L(r)(E,1)/r! |
Ω |
0.13722256529795 |
Real period |
R |
21.284125071794 |
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 |
69312cy1 8664d1 69312bm1 |
Quadratic twists by: -4 8 -19 |