Atkin-Lehner |
2+ 3- 5+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68400bk |
Isogeny class |
Conductor |
68400 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
122880 |
Modular degree for the optimal curve |
Δ |
-9972720000000 = -1 · 210 · 38 · 57 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -2 -4 2 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,5325,-26750] |
[a1,a2,a3,a4,a6] |
Generators |
[9:148:1] [35:-450:1] |
Generators of the group modulo torsion |
j |
1431644/855 |
j-invariant |
L |
9.8790926673508 |
L(r)(E,1)/r! |
Ω |
0.42301211902182 |
Real period |
R |
1.459634993759 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000017 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
34200cm1 22800w1 13680u1 |
Quadratic twists by: -4 -3 5 |