Atkin-Lehner |
2+ 5+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
68450k |
Isogeny class |
Conductor |
68450 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
380160 |
Modular degree for the optimal curve |
Δ |
136900000000000 = 211 · 511 · 372 |
Discriminant |
Eigenvalues |
2+ 3 5+ 0 2 -1 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-15667,506741] |
[a1,a2,a3,a4,a6] |
Generators |
[-82719:699022:729] |
Generators of the group modulo torsion |
j |
19882608489/6400000 |
j-invariant |
L |
8.6637143806296 |
L(r)(E,1)/r! |
Ω |
0.53827149526103 |
Real period |
R |
8.0477179793336 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000323 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
13690n1 68450bd1 |
Quadratic twists by: 5 37 |