Atkin-Lehner |
2- 3+ 7+ 37+ |
Signs for the Atkin-Lehner involutions |
Class |
49728cz |
Isogeny class |
Conductor |
49728 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
261120 |
Modular degree for the optimal curve |
Δ |
-4384004796186624 = -1 · 217 · 317 · 7 · 37 |
Discriminant |
Eigenvalues |
2- 3+ 3 7+ 0 2 -2 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-63649,-6932159] |
[a1,a2,a3,a4,a6] |
j |
-217568172289106/33447302217 |
j-invariant |
L |
2.3843845082571 |
L(r)(E,1)/r! |
Ω |
0.14902403175407 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
49728ci1 12432n1 |
Quadratic twists by: -4 8 |