Atkin-Lehner |
2- 3+ 5+ 7- |
Signs for the Atkin-Lehner involutions |
Class |
47040ef |
Isogeny class |
Conductor |
47040 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1474560 |
Modular degree for the optimal curve |
Δ |
3922370600400000000 = 210 · 35 · 58 · 79 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7- 0 6 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-5486301,-4943406915] |
[a1,a2,a3,a4,a6] |
Generators |
[1567170974526883:-153319489113266336:154249367147] |
Generators of the group modulo torsion |
j |
151591373397612544/32558203125 |
j-invariant |
L |
4.7127052161209 |
L(r)(E,1)/r! |
Ω |
0.098647307869093 |
Real period |
R |
23.886638763588 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999615 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
47040ch1 11760bg1 6720cl1 |
Quadratic twists by: -4 8 -7 |