Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696cr |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
Δ |
3054191732021624832 = 215 · 314 · 117 |
Discriminant |
Eigenvalues |
2+ 3- -2 0 11- -6 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-628716,-172476304] |
[a1,a2,a3,a4,a6] |
Generators |
[-440:4356:1] |
Generators of the group modulo torsion |
j |
649461896/72171 |
j-invariant |
L |
4.2363411019256 |
L(r)(E,1)/r! |
Ω |
0.17076935046336 |
Real period |
R |
1.5504615912 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000859 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696cq4 34848bz3 23232n4 6336p3 |
Quadratic twists by: -4 8 -3 -11 |