Atkin-Lehner |
2- 3+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
51984bu |
Isogeny class |
Conductor |
51984 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
-155952 = -1 · 24 · 33 · 192 |
Discriminant |
Eigenvalues |
2- 3+ 4 3 -4 -5 0 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1368,19475] |
[a1,a2,a3,a4,a6] |
Generators |
[25:30:1] |
Generators of the group modulo torsion |
j |
-1815478272 |
j-invariant |
L |
8.5433122325402 |
L(r)(E,1)/r! |
Ω |
2.6636521508492 |
Real period |
R |
1.6036839175481 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000025 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
12996h1 51984bv1 51984bl1 |
Quadratic twists by: -4 -3 -19 |