Atkin-Lehner |
3+ 7+ 19+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
86583c |
Isogeny class |
Conductor |
86583 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
309504 |
Modular degree for the optimal curve |
Δ |
-379170940491 = -1 · 32 · 74 · 19 · 314 |
Discriminant |
Eigenvalues |
-2 3+ -3 7+ -4 0 -5 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-32552,2271632] |
[a1,a2,a3,a4,a6] |
Generators |
[107:46:1] [-110:2123:1] |
Generators of the group modulo torsion |
j |
-1588831802134528/157922091 |
j-invariant |
L |
3.6345498062465 |
L(r)(E,1)/r! |
Ω |
0.9121173951787 |
Real period |
R |
0.49809238174321 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999997104 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
86583z1 |
Quadratic twists by: -7 |