Atkin-Lehner |
2+ 3+ 7- 19- |
Signs for the Atkin-Lehner involutions |
Class |
44688m |
Isogeny class |
Conductor |
44688 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
589824 |
Modular degree for the optimal curve |
Δ |
528075500409284688 = 24 · 316 · 79 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ 2 7- 4 -2 6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-213607,-14812622] |
[a1,a2,a3,a4,a6] |
Generators |
[509578409674634862:4207659717771211240:966159078853779] |
Generators of the group modulo torsion |
j |
572616640141312/280535480757 |
j-invariant |
L |
6.4606791638623 |
L(r)(E,1)/r! |
Ω |
0.23339347576378 |
Real period |
R |
27.681489993309 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000005 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
22344t1 6384n1 |
Quadratic twists by: -4 -7 |