Atkin-Lehner |
2+ 3- 7+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
51744ba |
Isogeny class |
Conductor |
51744 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
139776 |
Modular degree for the optimal curve |
Δ |
-779216621568 = -1 · 212 · 3 · 78 · 11 |
Discriminant |
Eigenvalues |
2+ 3- -2 7+ 11+ 6 3 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-36129,-2655633] |
[a1,a2,a3,a4,a6] |
j |
-220881472/33 |
j-invariant |
L |
2.770260833438 |
L(r)(E,1)/r! |
Ω |
0.17314130212498 |
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 |
51744bx1 103488h1 51744i1 |
Quadratic twists by: -4 8 -7 |