Atkin-Lehner |
2+ 7- 29- |
Signs for the Atkin-Lehner involutions |
Class |
12992t |
Isogeny class |
Conductor |
12992 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
-15898862092288 = -1 · 216 · 73 · 294 |
Discriminant |
Eigenvalues |
2+ -2 0 7- 0 -4 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-8513,355231] |
[a1,a2,a3,a4,a6] |
Generators |
[-51:812:1] |
Generators of the group modulo torsion |
j |
-1041220466500/242597383 |
j-invariant |
L |
2.9542162135466 |
L(r)(E,1)/r! |
Ω |
0.66547430247551 |
Real period |
R |
0.36993867914423 |
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 |
12992bc1 1624b1 116928bx1 90944by1 |
Quadratic twists by: -4 8 -3 -7 |