Atkin-Lehner |
2- 3- 5+ 7+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
37380h |
Isogeny class |
Conductor |
37380 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
172800 |
Modular degree for the optimal curve |
Δ |
381659238450000 = 24 · 36 · 55 · 76 · 89 |
Discriminant |
Eigenvalues |
2- 3- 5+ 7+ 4 -2 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-89621,-10313796] |
[a1,a2,a3,a4,a6] |
Generators |
[-173:207:1] |
Generators of the group modulo torsion |
j |
4975513762753675264/23853702403125 |
j-invariant |
L |
6.5793438934252 |
L(r)(E,1)/r! |
Ω |
0.27600821695588 |
Real period |
R |
2.648610314733 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
112140n1 |
Quadratic twists by: -3 |