Atkin-Lehner |
2- 3+ 5- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
22320z |
Isogeny class |
Conductor |
22320 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
48384 |
Modular degree for the optimal curve |
Δ |
-52714340352000 = -1 · 219 · 33 · 53 · 313 |
Discriminant |
Eigenvalues |
2- 3+ 5- 1 3 -4 6 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,8973,-122446] |
[a1,a2,a3,a4,a6] |
Generators |
[73:960:1] |
Generators of the group modulo torsion |
j |
722458663317/476656000 |
j-invariant |
L |
6.1957813322556 |
L(r)(E,1)/r! |
Ω |
0.35959151962383 |
Real period |
R |
0.71791892028129 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2790f1 89280dc1 22320t2 111600cj1 |
Quadratic twists by: -4 8 -3 5 |