Atkin-Lehner |
2+ 7- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
12992p |
Isogeny class |
Conductor |
12992 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
3584 |
Modular degree for the optimal curve |
Δ |
-90944 = -1 · 26 · 72 · 29 |
Discriminant |
Eigenvalues |
2+ 3 3 7- 3 1 -8 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-31,68] |
[a1,a2,a3,a4,a6] |
j |
-51478848/1421 |
j-invariant |
L |
6.7627774931979 |
L(r)(E,1)/r! |
Ω |
3.3813887465989 |
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 |
12992e1 6496l1 116928co1 90944bi1 |
Quadratic twists by: -4 8 -3 -7 |