Atkin-Lehner |
2+ 3+ 5+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
40200d |
Isogeny class |
Conductor |
40200 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
67968 |
Modular degree for the optimal curve |
Δ |
-155915539200 = -1 · 28 · 34 · 52 · 673 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 0 2 -6 -3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-15233,728997] |
[a1,a2,a3,a4,a6] |
Generators |
[-127:774:1] [143:-1206:1] |
Generators of the group modulo torsion |
j |
-61084155520000/24361803 |
j-invariant |
L |
7.8988891729521 |
L(r)(E,1)/r! |
Ω |
1.0077712755937 |
Real period |
R |
0.32658242021476 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
80400u1 120600bs1 40200bj1 |
Quadratic twists by: -4 -3 5 |