Atkin-Lehner |
2+ 3+ 5+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68400a |
Isogeny class |
Conductor |
68400 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
2052000000 = 28 · 33 · 56 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 0 2 2 4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-375,1750] |
[a1,a2,a3,a4,a6] |
Generators |
[21:56:1] |
Generators of the group modulo torsion |
j |
54000/19 |
j-invariant |
L |
6.8922182845751 |
L(r)(E,1)/r! |
Ω |
1.349876239618 |
Real period |
R |
2.5529074747305 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000597 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
34200i1 68400b1 2736a1 |
Quadratic twists by: -4 -3 5 |