Atkin-Lehner |
2- 3- 5+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
60840bk |
Isogeny class |
Conductor |
60840 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
1916928 |
Modular degree for the optimal curve |
Δ |
-7136012347308000000 = -1 · 28 · 37 · 56 · 138 |
Discriminant |
Eigenvalues |
2- 3- 5+ -1 2 13+ -6 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-6511908,6397321268] |
[a1,a2,a3,a4,a6] |
Generators |
[1444:-2250:1] |
Generators of the group modulo torsion |
j |
-200601496576/46875 |
j-invariant |
L |
5.8496725095638 |
L(r)(E,1)/r! |
Ω |
0.22967404861953 |
Real period |
R |
1.5918408459345 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000011 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
121680o1 20280h1 60840t1 |
Quadratic twists by: -4 -3 13 |