Atkin-Lehner |
5+ 7+ 17- 23- |
Signs for the Atkin-Lehner involutions |
Class |
68425b |
Isogeny class |
Conductor |
68425 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
147456 |
Modular degree for the optimal curve |
Δ |
11359619140625 = 512 · 7 · 172 · 23 |
Discriminant |
Eigenvalues |
1 0 5+ 7+ 6 4 17- -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-17792,-894509] |
[a1,a2,a3,a4,a6] |
Generators |
[-1440558:-1400021:19683] |
Generators of the group modulo torsion |
j |
39864996115281/727015625 |
j-invariant |
L |
7.5126766841121 |
L(r)(E,1)/r! |
Ω |
0.41383099312956 |
Real period |
R |
9.0769865101654 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998155 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
13685e1 |
Quadratic twists by: 5 |