Atkin-Lehner |
2+ 3- 7+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
31248n |
Isogeny class |
Conductor |
31248 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
10240 |
Modular degree for the optimal curve |
Δ |
-283481856 = -1 · 28 · 36 · 72 · 31 |
Discriminant |
Eigenvalues |
2+ 3- -2 7+ -6 0 -4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,9,-810] |
[a1,a2,a3,a4,a6] |
Generators |
[18:72:1] |
Generators of the group modulo torsion |
j |
432/1519 |
j-invariant |
L |
3.3720490664061 |
L(r)(E,1)/r! |
Ω |
0.80389374829051 |
Real period |
R |
2.0973226086014 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
15624n1 124992fb1 3472a1 |
Quadratic twists by: -4 8 -3 |