Atkin-Lehner |
2- 3+ 5+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
121680cn |
Isogeny class |
Conductor |
121680 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
50688 |
Modular degree for the optimal curve |
Δ |
-186900480 = -1 · 213 · 33 · 5 · 132 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -4 5 13+ -2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,117,442] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:8:1] [-1:18:1] |
Generators of the group modulo torsion |
j |
9477/10 |
j-invariant |
L |
10.485553888626 |
L(r)(E,1)/r! |
Ω |
1.1887575330227 |
Real period |
R |
1.1025749147779 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.000000000316 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
15210bb1 121680da1 121680cy1 |
Quadratic twists by: -4 -3 13 |