Atkin-Lehner |
2+ 23- 59- |
Signs for the Atkin-Lehner involutions |
Class |
21712d |
Isogeny class |
Conductor |
21712 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
2432 |
Modular degree for the optimal curve |
Δ |
-1281008 = -1 · 24 · 23 · 592 |
Discriminant |
Eigenvalues |
2+ 1 0 0 6 -3 0 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-28,-89] |
[a1,a2,a3,a4,a6] |
Generators |
[21:95:1] |
Generators of the group modulo torsion |
j |
-157216000/80063 |
j-invariant |
L |
6.4724310938176 |
L(r)(E,1)/r! |
Ω |
1.0103401591157 |
Real period |
R |
3.2030950345884 |
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 |
10856c1 86848x1 |
Quadratic twists by: -4 8 |