Atkin-Lehner |
2- 3+ 5- 7+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
21840bk |
Isogeny class |
Conductor |
21840 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
221184 |
Modular degree for the optimal curve |
Δ |
47719177519104000 = 224 · 36 · 53 · 74 · 13 |
Discriminant |
Eigenvalues |
2- 3+ 5- 7+ 0 13- 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-411600,-100957248] |
[a1,a2,a3,a4,a6] |
j |
1882742462388824401/11650189824000 |
j-invariant |
L |
2.2626831796096 |
L(r)(E,1)/r! |
Ω |
0.18855693163413 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
2730bd1 87360fu1 65520cq1 109200fz1 |
Quadratic twists by: -4 8 -3 5 |