Atkin-Lehner |
2+ 17+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
8432a |
Isogeny class |
Conductor |
8432 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
21312 |
Modular degree for the optimal curve |
Δ |
-11972234224 = -1 · 24 · 176 · 31 |
Discriminant |
Eigenvalues |
2+ 0 3 -3 4 -4 17+ -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-72791,-7559007] |
[a1,a2,a3,a4,a6] |
Generators |
[440394892704:-5041943271899:1167575877] |
Generators of the group modulo torsion |
j |
-2665856613954845952/748264639 |
j-invariant |
L |
4.6352206682411 |
L(r)(E,1)/r! |
Ω |
0.14532827888781 |
Real period |
R |
15.947414721052 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4216d1 33728j1 75888k1 |
Quadratic twists by: -4 8 -3 |