Atkin-Lehner |
23- 41- |
Signs for the Atkin-Lehner involutions |
Class |
21689c |
Isogeny class |
Conductor |
21689 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
1920 |
Modular degree for the optimal curve |
Δ |
-498847 = -1 · 233 · 41 |
Discriminant |
Eigenvalues |
-1 -2 0 0 -4 2 6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,12,31] |
[a1,a2,a3,a4,a6] |
Generators |
[2:7:1] |
Generators of the group modulo torsion |
j |
15625/41 |
j-invariant |
L |
1.8329077407655 |
L(r)(E,1)/r! |
Ω |
2.0608922078219 |
Real period |
R |
1.778751682217 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
21689b1 |
Quadratic twists by: -23 |