Atkin-Lehner |
3+ 7- 19+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
86583g |
Isogeny class |
Conductor |
86583 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
2365440 |
Modular degree for the optimal curve |
Δ |
-6092568297771972723 = -1 · 322 · 73 · 19 · 313 |
Discriminant |
Eigenvalues |
2 3+ -2 7- 0 0 -5 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,281846,-103950981] |
[a1,a2,a3,a4,a6] |
Generators |
[28986:1761267:8] [132676:6200113:64] |
Generators of the group modulo torsion |
j |
7218777866541756416/17762589789422661 |
j-invariant |
L |
16.008791366256 |
L(r)(E,1)/r! |
Ω |
0.12338513204925 |
Real period |
R |
32.436629723488 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999997472 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
86583bc1 |
Quadratic twists by: -7 |