Atkin-Lehner |
2+ 3+ 19+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
3534b |
Isogeny class |
Conductor |
3534 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
9216 |
Modular degree for the optimal curve |
Δ |
-210012812784 = -1 · 24 · 32 · 196 · 31 |
Discriminant |
Eigenvalues |
2+ 3+ 2 -4 -6 0 -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-9139,-340835] |
[a1,a2,a3,a4,a6] |
j |
-84429456495634873/210012812784 |
j-invariant |
L |
0.48820697844269 |
L(r)(E,1)/r! |
Ω |
0.24410348922135 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
28272j1 113088r1 10602h1 88350cp1 |
Quadratic twists by: -4 8 -3 5 |