Atkin-Lehner |
2+ 3+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
27072c |
Isogeny class |
Conductor |
27072 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
2560 |
Modular degree for the optimal curve |
Δ |
81216 = 26 · 33 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ 3 1 -3 0 0 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-36,82] |
[a1,a2,a3,a4,a6] |
Generators |
[3:1:1] |
Generators of the group modulo torsion |
j |
2985984/47 |
j-invariant |
L |
6.9247548520323 |
L(r)(E,1)/r! |
Ω |
3.4302114860293 |
Real period |
R |
1.0093772468892 |
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 |
27072bt1 423g1 27072h1 |
Quadratic twists by: -4 8 -3 |