Atkin-Lehner |
2+ 3- 5- 13- |
Signs for the Atkin-Lehner involutions |
Class |
60840bc |
Isogeny class |
Conductor |
60840 |
Conductor |
∏ cp |
160 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-3843871200000 = -1 · 28 · 37 · 55 · 133 |
Discriminant |
Eigenvalues |
2+ 3- 5- -3 -3 13- -1 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-15132,722644] |
[a1,a2,a3,a4,a6] |
Generators |
[-142:90:1] [-52:-1170:1] |
Generators of the group modulo torsion |
j |
-934577152/9375 |
j-invariant |
L |
9.8073548066119 |
L(r)(E,1)/r! |
Ω |
0.78855770338838 |
Real period |
R |
0.077731746551938 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999936 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
121680cb1 20280ba1 60840bo1 |
Quadratic twists by: -4 -3 13 |