Atkin-Lehner |
2- 3+ 5+ 7+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
57120bi |
Isogeny class |
Conductor |
57120 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
122880 |
Modular degree for the optimal curve |
Δ |
-32799375000000 = -1 · 26 · 32 · 510 · 73 · 17 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7+ -2 2 17- -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-4306,-294800] |
[a1,a2,a3,a4,a6] |
Generators |
[3786:232888:1] |
Generators of the group modulo torsion |
j |
-137996054243776/512490234375 |
j-invariant |
L |
4.2656379542967 |
L(r)(E,1)/r! |
Ω |
0.26981834176354 |
Real period |
R |
7.9046478575754 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999654 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
57120t1 114240eg1 |
Quadratic twists by: -4 8 |