Atkin-Lehner |
2+ 7+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
12992a |
Isogeny class |
Conductor |
12992 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
1664 |
Modular degree for the optimal curve |
Δ |
376768 = 26 · 7 · 292 |
Discriminant |
Eigenvalues |
2+ 0 2 7+ 6 -2 -4 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-19,-12] |
[a1,a2,a3,a4,a6] |
Generators |
[-156:285:64] |
Generators of the group modulo torsion |
j |
11852352/5887 |
j-invariant |
L |
5.2384700412288 |
L(r)(E,1)/r! |
Ω |
2.4068624761077 |
Real period |
R |
4.3529450421283 |
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 |
12992k1 6496c2 116928bs1 90944o1 |
Quadratic twists by: -4 8 -3 -7 |