Atkin-Lehner |
2+ 3- 13+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
69264g |
Isogeny class |
Conductor |
69264 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
98304 |
Modular degree for the optimal curve |
Δ |
151328887632 = 24 · 312 · 13 · 372 |
Discriminant |
Eigenvalues |
2+ 3- 0 0 -2 13+ -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-53310,-4737593] |
[a1,a2,a3,a4,a6] |
Generators |
[144456:838309:512] |
Generators of the group modulo torsion |
j |
1436488814848000/12974013 |
j-invariant |
L |
5.267630900584 |
L(r)(E,1)/r! |
Ω |
0.31419380619153 |
Real period |
R |
8.3827733015591 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000089 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
34632c1 23088g1 |
Quadratic twists by: -4 -3 |