Atkin-Lehner |
2+ 3+ 5+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
21960a |
Isogeny class |
Conductor |
21960 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
3840 |
Modular degree for the optimal curve |
Δ |
-2108160 = -1 · 28 · 33 · 5 · 61 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 1 -4 -2 -8 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,12,68] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:6:1] [1:9:1] |
Generators of the group modulo torsion |
j |
27648/305 |
j-invariant |
L |
7.2459206227795 |
L(r)(E,1)/r! |
Ω |
1.9225880512158 |
Real period |
R |
0.47110460156795 |
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 |
43920a1 21960m1 109800be1 |
Quadratic twists by: -4 -3 5 |