Atkin-Lehner |
3- 5- 13+ 53- |
Signs for the Atkin-Lehner involutions |
Class |
31005p |
Isogeny class |
Conductor |
31005 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
399360 |
Modular degree for the optimal curve |
Δ |
-84584304674341875 = -1 · 319 · 54 · 133 · 53 |
Discriminant |
Eigenvalues |
2 3- 5- -2 -5 13+ -4 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-31197,14152567] |
[a1,a2,a3,a4,a6] |
j |
-4606114001711104/116027852776875 |
j-invariant |
L |
2.286378979083 |
L(r)(E,1)/r! |
Ω |
0.28579737238573 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10335b1 |
Quadratic twists by: -3 |