Atkin-Lehner |
2+ 3+ 7- 19- |
Signs for the Atkin-Lehner involutions |
Class |
67032h |
Isogeny class |
Conductor |
67032 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
258048 |
Modular degree for the optimal curve |
Δ |
-13375398102192 = -1 · 24 · 39 · 76 · 192 |
Discriminant |
Eigenvalues |
2+ 3+ 4 7- 6 -2 4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-7938,-324135] |
[a1,a2,a3,a4,a6] |
Generators |
[7490:228095:8] |
Generators of the group modulo torsion |
j |
-1492992/361 |
j-invariant |
L |
9.7190273084717 |
L(r)(E,1)/r! |
Ω |
0.24970679618948 |
Real period |
R |
4.8652196575775 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000882 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
67032bp1 1368a1 |
Quadratic twists by: -3 -7 |