Atkin-Lehner |
2+ 3- 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
60192g |
Isogeny class |
Conductor |
60192 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
-2293693687296 = -1 · 29 · 311 · 113 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 1 2 11- 4 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1587,-76822] |
[a1,a2,a3,a4,a6] |
Generators |
[58:162:1] |
Generators of the group modulo torsion |
j |
-1184287112/6145227 |
j-invariant |
L |
8.2565020652027 |
L(r)(E,1)/r! |
Ω |
0.34081366282565 |
Real period |
R |
2.018821173598 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000043 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
60192d1 120384cw1 20064n1 |
Quadratic twists by: -4 8 -3 |