Atkin-Lehner |
2+ 7+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
33712a |
Isogeny class |
Conductor |
33712 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
43008 |
Modular degree for the optimal curve |
Δ |
170545872784 = 24 · 78 · 432 |
Discriminant |
Eigenvalues |
2+ -1 -3 7+ 5 -6 -1 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-2172,-32801] |
[a1,a2,a3,a4,a6] |
Generators |
[-33:43:1] |
Generators of the group modulo torsion |
j |
12291328/1849 |
j-invariant |
L |
2.4734963028328 |
L(r)(E,1)/r! |
Ω |
0.70635936572099 |
Real period |
R |
1.7508766945481 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999978 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16856b1 33712e1 |
Quadratic twists by: -4 -7 |