Atkin-Lehner |
2- 3+ 17- 37- |
Signs for the Atkin-Lehner involutions |
Class |
60384w |
Isogeny class |
Conductor |
60384 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
36864 |
Modular degree for the optimal curve |
Δ |
-31743627264 = -1 · 212 · 32 · 17 · 373 |
Discriminant |
Eigenvalues |
2- 3+ -1 -3 -1 -2 17- -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-2401,46897] |
[a1,a2,a3,a4,a6] |
Generators |
[-56:51:1] [-21:296:1] |
Generators of the group modulo torsion |
j |
-373870425664/7749909 |
j-invariant |
L |
7.3440507317566 |
L(r)(E,1)/r! |
Ω |
1.1707528141469 |
Real period |
R |
0.5227441866895 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000011 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
60384bb1 120768dm1 |
Quadratic twists by: -4 8 |