Atkin-Lehner |
2+ 3+ 23- 59- |
Signs for the Atkin-Lehner involutions |
Class |
8142b |
Isogeny class |
Conductor |
8142 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
2304 |
Modular degree for the optimal curve |
Δ |
-16674816 = -1 · 212 · 3 · 23 · 59 |
Discriminant |
Eigenvalues |
2+ 3+ -2 -4 0 2 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,64,0] |
[a1,a2,a3,a4,a6] |
Generators |
[9:33:1] |
Generators of the group modulo torsion |
j |
28288984823/16674816 |
j-invariant |
L |
1.7263163046631 |
L(r)(E,1)/r! |
Ω |
1.2885772669288 |
Real period |
R |
2.6794144968545 |
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 |
65136s1 24426k1 |
Quadratic twists by: -4 -3 |