Atkin-Lehner |
2+ 3- 37+ 41- |
Signs for the Atkin-Lehner involutions |
Class |
27306d |
Isogeny class |
Conductor |
27306 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
8704 |
Modular degree for the optimal curve |
Δ |
-272049678 = -1 · 2 · 37 · 37 · 412 |
Discriminant |
Eigenvalues |
2+ 3- -2 1 3 -1 -5 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,162,-86] |
[a1,a2,a3,a4,a6] |
Generators |
[3:19:1] |
Generators of the group modulo torsion |
j |
642735647/373182 |
j-invariant |
L |
3.2380346118827 |
L(r)(E,1)/r! |
Ω |
1.0315802518534 |
Real period |
R |
0.78472678351125 |
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 |
9102e1 |
Quadratic twists by: -3 |