Atkin-Lehner |
2+ 3+ 7- 67- |
Signs for the Atkin-Lehner involutions |
Class |
33768b |
Isogeny class |
Conductor |
33768 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
2560 |
Modular degree for the optimal curve |
Δ |
-202608 = -1 · 24 · 33 · 7 · 67 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7- -1 1 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,9,19] |
[a1,a2,a3,a4,a6] |
Generators |
[-1:3:1] |
Generators of the group modulo torsion |
j |
186624/469 |
j-invariant |
L |
4.7193570727316 |
L(r)(E,1)/r! |
Ω |
2.2170146972415 |
Real period |
R |
0.53217476169686 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999995 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
67536e1 33768m1 |
Quadratic twists by: -4 -3 |