Atkin-Lehner |
2- 3+ 13+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
82524a |
Isogeny class |
Conductor |
82524 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1824768 |
Modular degree for the optimal curve |
Δ |
8656475012373743568 = 24 · 312 · 13 · 238 |
Discriminant |
Eigenvalues |
2- 3+ 0 0 4 13+ -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-2958873,-1952907282] |
[a1,a2,a3,a4,a6] |
Generators |
[-2278212714240808222:-4956864449554500464:2327730853071889] |
Generators of the group modulo torsion |
j |
1209527744512000/3654719757 |
j-invariant |
L |
5.7778216156394 |
L(r)(E,1)/r! |
Ω |
0.11513221190231 |
Real period |
R |
25.092115926884 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999994754 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
3588a1 |
Quadratic twists by: -23 |