Atkin-Lehner |
3+ 5- 89- |
Signs for the Atkin-Lehner involutions |
Class |
4005b |
Isogeny class |
Conductor |
4005 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1728 |
Modular degree for the optimal curve |
Δ |
-1094866875 = -1 · 39 · 54 · 89 |
Discriminant |
Eigenvalues |
0 3+ 5- -4 2 4 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,108,1532] |
[a1,a2,a3,a4,a6] |
Generators |
[12:67:1] |
Generators of the group modulo torsion |
j |
7077888/55625 |
j-invariant |
L |
2.897428929807 |
L(r)(E,1)/r! |
Ω |
1.1310561823516 |
Real period |
R |
0.32021275501353 |
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 |
64080p1 4005a1 20025d1 |
Quadratic twists by: -4 -3 5 |