Atkin-Lehner |
3- 11+ 17+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
31977g |
Isogeny class |
Conductor |
31977 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
7168 |
Modular degree for the optimal curve |
Δ |
-442913427 = -1 · 38 · 11 · 17 · 192 |
Discriminant |
Eigenvalues |
0 3- 0 1 11+ -4 17+ 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,150,-725] |
[a1,a2,a3,a4,a6] |
Generators |
[50:167:8] [11:47:1] |
Generators of the group modulo torsion |
j |
512000000/607563 |
j-invariant |
L |
7.3907947259035 |
L(r)(E,1)/r! |
Ω |
0.89775197223409 |
Real period |
R |
2.058139373259 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999998 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10659b1 |
Quadratic twists by: -3 |