Atkin-Lehner |
2- 19- 103- |
Signs for the Atkin-Lehner involutions |
Class |
31312s |
Isogeny class |
Conductor |
31312 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
1728 |
Modular degree for the optimal curve |
Δ |
31312 = 24 · 19 · 103 |
Discriminant |
Eigenvalues |
2- 1 -2 1 0 -6 -2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-9,-10] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:2:1] [26:19:8] |
Generators of the group modulo torsion |
j |
5619712/1957 |
j-invariant |
L |
8.7915677043715 |
L(r)(E,1)/r! |
Ω |
2.8093265348034 |
Real period |
R |
3.1294218010821 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999992 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7828a1 125248bc1 |
Quadratic twists by: -4 8 |