Atkin-Lehner |
2+ 11+ 67+ |
Signs for the Atkin-Lehner involutions |
Class |
129712a |
Isogeny class |
Conductor |
129712 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
91317248 = 210 · 113 · 67 |
Discriminant |
Eigenvalues |
2+ 0 0 0 11+ 2 4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-275,-1694] |
[a1,a2,a3,a4,a6] |
Generators |
[25:84:1] |
Generators of the group modulo torsion |
j |
1687500/67 |
j-invariant |
L |
5.8793157187943 |
L(r)(E,1)/r! |
Ω |
1.1752438778125 |
Real period |
R |
2.5013173251168 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999543732 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
64856g1 129712b1 |
Quadratic twists by: -4 -11 |