Atkin-Lehner |
2- 3- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
69312cy |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
18 |
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 |
[-241:4332:1] |
Generators of the group modulo torsion |
j |
-4864000/27 |
j-invariant |
L |
7.2119903104708 |
L(r)(E,1)/r! |
Ω |
0.52876631869701 |
Real period |
R |
0.75773761336753 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000022 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69312a1 17328a1 69312cl1 |
Quadratic twists by: -4 8 -19 |