Atkin-Lehner |
2- 3+ 7+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
121968ct |
Isogeny class |
Conductor |
121968 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
-749371392 = -1 · 215 · 33 · 7 · 112 |
Discriminant |
Eigenvalues |
2- 3+ 4 7+ 11- 1 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-363,2970] |
[a1,a2,a3,a4,a6] |
Generators |
[15:30:1] |
Generators of the group modulo torsion |
j |
-395307/56 |
j-invariant |
L |
9.7776986036476 |
L(r)(E,1)/r! |
Ω |
1.5474152987297 |
Real period |
R |
1.5796823575654 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000015062 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
15246bd1 121968cv1 121968df1 |
Quadratic twists by: -4 -3 -11 |