Atkin-Lehner |
2- 7+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
129472cn |
Isogeny class |
Conductor |
129472 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
940032 |
Modular degree for the optimal curve |
Δ |
-78403495600553984 = -1 · 215 · 73 · 178 |
Discriminant |
Eigenvalues |
2- -1 -1 7+ -4 1 17- -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-111361,19686209] |
[a1,a2,a3,a4,a6] |
Generators |
[193:-2312:1] |
Generators of the group modulo torsion |
j |
-668168/343 |
j-invariant |
L |
1.8483046701429 |
L(r)(E,1)/r! |
Ω |
0.31964451340482 |
Real period |
R |
0.48186465686747 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999997018149 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
129472dp1 64736p1 129472cw1 |
Quadratic twists by: -4 8 17 |