Atkin-Lehner |
3+ 5- 23- 71- |
Signs for the Atkin-Lehner involutions |
Class |
122475o |
Isogeny class |
Conductor |
122475 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
2606400 |
Modular degree for the optimal curve |
Δ |
1414727473243359375 = 310 · 58 · 233 · 712 |
Discriminant |
Eigenvalues |
-1 3+ 5- -1 -5 -5 -6 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-1404013,637184156] |
[a1,a2,a3,a4,a6] |
Generators |
[-6770:282831:8] [160:20332:1] |
Generators of the group modulo torsion |
j |
783568707666901105/3621702331503 |
j-invariant |
L |
5.0115244219967 |
L(r)(E,1)/r! |
Ω |
0.2711685000478 |
Real period |
R |
0.51336719293125 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000002961 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
122475r1 |
Quadratic twists by: 5 |