Atkin-Lehner |
2+ 3+ 7- 29- |
Signs for the Atkin-Lehner involutions |
Class |
68208l |
Isogeny class |
Conductor |
68208 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
110592 |
Modular degree for the optimal curve |
Δ |
-2507115249072 = -1 · 24 · 38 · 77 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ 2 7- 0 -6 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,1993,-68718] |
[a1,a2,a3,a4,a6] |
Generators |
[137572482:1842329440:804357] |
Generators of the group modulo torsion |
j |
464857088/1331883 |
j-invariant |
L |
5.1817713049682 |
L(r)(E,1)/r! |
Ω |
0.41748277844063 |
Real period |
R |
12.411940257796 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000588 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
34104t1 9744g1 |
Quadratic twists by: -4 -7 |