Atkin-Lehner |
2- 3+ 5- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
60840bi |
Isogeny class |
Conductor |
60840 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
322560 |
Modular degree for the optimal curve |
Δ |
-1580901196942080 = -1 · 28 · 39 · 5 · 137 |
Discriminant |
Eigenvalues |
2- 3+ 5- -3 -5 13+ -3 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-18252,-2135484] |
[a1,a2,a3,a4,a6] |
Generators |
[585:13689:1] |
Generators of the group modulo torsion |
j |
-27648/65 |
j-invariant |
L |
5.1103226180303 |
L(r)(E,1)/r! |
Ω |
0.19176780508962 |
Real period |
R |
1.665530684115 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000775 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
121680i1 60840a1 4680a1 |
Quadratic twists by: -4 -3 13 |