Atkin-Lehner |
2+ 3+ 19+ 83- |
Signs for the Atkin-Lehner involutions |
Class |
75696a |
Isogeny class |
Conductor |
75696 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
-301572864 = -1 · 28 · 32 · 19 · 832 |
Discriminant |
Eigenvalues |
2+ 3+ -1 -1 -3 0 -1 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-81,909] |
[a1,a2,a3,a4,a6] |
Generators |
[20:-83:1] [12:39:1] |
Generators of the group modulo torsion |
j |
-232428544/1178019 |
j-invariant |
L |
8.2679980550511 |
L(r)(E,1)/r! |
Ω |
1.4960919389996 |
Real period |
R |
1.3815992586443 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998897 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
37848c1 |
Quadratic twists by: -4 |