Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696de |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
540672 |
Modular degree for the optimal curve |
Δ |
-10241155022782464 = -1 · 216 · 36 · 118 |
Discriminant |
Eigenvalues |
2+ 3- 3 4 11- -3 -3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-47916,6324912] |
[a1,a2,a3,a4,a6] |
Generators |
[-242:1936:1] |
Generators of the group modulo torsion |
j |
-1188 |
j-invariant |
L |
9.4133963864426 |
L(r)(E,1)/r! |
Ω |
0.37256813524891 |
Real period |
R |
1.0527600519623 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000028 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69696gu1 8712z1 7744d1 69696df1 |
Quadratic twists by: -4 8 -3 -11 |