Atkin-Lehner |
2- 3+ 5+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
22320w |
Isogeny class |
Conductor |
22320 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
20736 |
Modular degree for the optimal curve |
Δ |
-99970744320 = -1 · 215 · 39 · 5 · 31 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 3 -5 0 2 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-243,15282] |
[a1,a2,a3,a4,a6] |
Generators |
[57:432:1] |
Generators of the group modulo torsion |
j |
-19683/1240 |
j-invariant |
L |
5.2291379747314 |
L(r)(E,1)/r! |
Ω |
0.87923491691398 |
Real period |
R |
0.74342162062403 |
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 |
2790b1 89280du1 22320bc1 111600cy1 |
Quadratic twists by: -4 8 -3 5 |