Atkin-Lehner |
3+ 5+ 7- 23- |
Signs for the Atkin-Lehner involutions |
Class |
12075i |
Isogeny class |
Conductor |
12075 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
127353515625 = 34 · 510 · 7 · 23 |
Discriminant |
Eigenvalues |
1 3+ 5+ 7- 0 -2 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-7000,221875] |
[a1,a2,a3,a4,a6] |
Generators |
[30:185:1] |
Generators of the group modulo torsion |
j |
2428257525121/8150625 |
j-invariant |
L |
4.6006509901413 |
L(r)(E,1)/r! |
Ω |
1.0470495409166 |
Real period |
R |
2.1969595565238 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
36225bo1 2415h1 84525cj1 |
Quadratic twists by: -3 5 -7 |