Atkin-Lehner |
2- 3+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
27072bs |
Isogeny class |
Conductor |
27072 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
5120 |
Modular degree for the optimal curve |
Δ |
3817152 = 26 · 33 · 472 |
Discriminant |
Eigenvalues |
2- 3+ -2 -4 -4 -6 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-51,-104] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:6:1] |
Generators of the group modulo torsion |
j |
8489664/2209 |
j-invariant |
L |
2.3910408262005 |
L(r)(E,1)/r! |
Ω |
1.8209664156288 |
Real period |
R |
1.3130614632312 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
27072bm1 13536w2 27072bl1 |
Quadratic twists by: -4 8 -3 |