Atkin-Lehner |
2- 3+ 5+ 7- |
Signs for the Atkin-Lehner involutions |
Class |
47040eo |
Isogeny class |
Conductor |
47040 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
442368 |
Modular degree for the optimal curve |
Δ |
146496183735384000 = 26 · 33 · 53 · 714 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7- -4 2 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-259716,47586330] |
[a1,a2,a3,a4,a6] |
Generators |
[8729747:545880574:2197] |
Generators of the group modulo torsion |
j |
257307998572864/19456203375 |
j-invariant |
L |
4.284889707257 |
L(r)(E,1)/r! |
Ω |
0.31894084339074 |
Real period |
R |
13.434747527811 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999891 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
47040ge1 23520v3 6720cm1 |
Quadratic twists by: -4 8 -7 |