Atkin-Lehner |
2- 3- 5+ 7+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
69300y |
Isogeny class |
Conductor |
69300 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
349440 |
Modular degree for the optimal curve |
Δ |
-22373533239750000 = -1 · 24 · 319 · 56 · 7 · 11 |
Discriminant |
Eigenvalues |
2- 3- 5+ 7+ 11+ 1 0 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-105825,15078625] |
[a1,a2,a3,a4,a6] |
Generators |
[416:6561:1] |
Generators of the group modulo torsion |
j |
-719152519936/122762871 |
j-invariant |
L |
6.425492235864 |
L(r)(E,1)/r! |
Ω |
0.36691138846461 |
Real period |
R |
1.4593651307304 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999986716 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23100w1 2772j1 |
Quadratic twists by: -3 5 |