Atkin-Lehner |
2- 5+ 7+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
49840i |
Isogeny class |
Conductor |
49840 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
245760 |
Modular degree for the optimal curve |
Δ |
8547560000000000 = 212 · 510 · 74 · 89 |
Discriminant |
Eigenvalues |
2- 0 5+ 7+ 0 -4 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-54563,-2068638] |
[a1,a2,a3,a4,a6] |
Generators |
[-201:882:1] [-103:1568:1] |
Generators of the group modulo torsion |
j |
4385897588651769/2086806640625 |
j-invariant |
L |
8.4659985422993 |
L(r)(E,1)/r! |
Ω |
0.32735133207819 |
Real period |
R |
6.4655293202506 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
3115b1 |
Quadratic twists by: -4 |