Atkin-Lehner |
2+ 3+ 5+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
58560d |
Isogeny class |
Conductor |
58560 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
32768 |
Modular degree for the optimal curve |
Δ |
3162240000 = 210 · 34 · 54 · 61 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ -4 0 2 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-381,-819] |
[a1,a2,a3,a4,a6] |
Generators |
[-15:36:1] |
Generators of the group modulo torsion |
j |
5988775936/3088125 |
j-invariant |
L |
3.1353091741828 |
L(r)(E,1)/r! |
Ω |
1.1424119592386 |
Real period |
R |
1.3722322970675 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000434 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
58560di1 7320q1 |
Quadratic twists by: -4 8 |