Atkin-Lehner |
2+ 3+ 17+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
60384b |
Isogeny class |
Conductor |
60384 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
-16903655424 = -1 · 212 · 38 · 17 · 37 |
Discriminant |
Eigenvalues |
2+ 3+ -1 -1 3 -4 17+ -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,479,-4943] |
[a1,a2,a3,a4,a6] |
Generators |
[9:4:1] [16:81:1] |
Generators of the group modulo torsion |
j |
2961169856/4126869 |
j-invariant |
L |
8.2126532834888 |
L(r)(E,1)/r! |
Ω |
0.65595921300828 |
Real period |
R |
1.5650083725916 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999954 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
60384n1 120768cz1 |
Quadratic twists by: -4 8 |