Atkin-Lehner |
2+ 7+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
12992b |
Isogeny class |
Conductor |
12992 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-95361695744 = -1 · 226 · 72 · 29 |
Discriminant |
Eigenvalues |
2+ 1 3 7+ 1 1 -4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-6529,201439] |
[a1,a2,a3,a4,a6] |
Generators |
[45:28:1] |
Generators of the group modulo torsion |
j |
-117433042273/363776 |
j-invariant |
L |
6.5097318294725 |
L(r)(E,1)/r! |
Ω |
1.072224367129 |
Real period |
R |
1.5178100845868 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
12992bh1 406c1 116928bt1 90944z1 |
Quadratic twists by: -4 8 -3 -7 |