Atkin-Lehner |
2- 3+ 11+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
68112ba |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
5760 |
Modular degree for the optimal curve |
Δ |
-204336 = -1 · 24 · 33 · 11 · 43 |
Discriminant |
Eigenvalues |
2- 3+ 1 -3 11+ -4 -5 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-12,27] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:6:1] [1:4:1] |
Generators of the group modulo torsion |
j |
-442368/473 |
j-invariant |
L |
10.007559569038 |
L(r)(E,1)/r! |
Ω |
2.8801860425591 |
Real period |
R |
1.7373113092598 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000018 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17028c1 68112bf1 |
Quadratic twists by: -4 -3 |