Atkin-Lehner |
2- 13+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
83824z |
Isogeny class |
Conductor |
83824 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
389376 |
Modular degree for the optimal curve |
Δ |
12053511219018256 = 24 · 138 · 314 |
Discriminant |
Eigenvalues |
2- 1 2 -1 1 13+ 7 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-66642,-4015465] |
[a1,a2,a3,a4,a6] |
Generators |
[-45304:560015:512] |
Generators of the group modulo torsion |
j |
2507884288/923521 |
j-invariant |
L |
8.6610552076258 |
L(r)(E,1)/r! |
Ω |
0.30633968828578 |
Real period |
R |
7.0681791631441 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001482 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
20956a1 83824p1 |
Quadratic twists by: -4 13 |