Atkin-Lehner |
2+ 11+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
11968b |
Isogeny class |
Conductor |
11968 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
2304 |
Modular degree for the optimal curve |
Δ |
-24618176 = -1 · 26 · 113 · 172 |
Discriminant |
Eigenvalues |
2+ -1 -3 2 11+ -2 17+ -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,43,199] |
[a1,a2,a3,a4,a6] |
Generators |
[2:17:1] |
Generators of the group modulo torsion |
j |
134217728/384659 |
j-invariant |
L |
2.7181796130823 |
L(r)(E,1)/r! |
Ω |
1.4952741110716 |
Real period |
R |
0.9089235187568 |
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 |
11968u1 187a1 107712cp1 |
Quadratic twists by: -4 8 -3 |