Atkin-Lehner |
2+ 3+ 7+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
39984a |
Isogeny class |
Conductor |
39984 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
56448 |
Modular degree for the optimal curve |
Δ |
-1279509111552 = -1 · 28 · 3 · 78 · 172 |
Discriminant |
Eigenvalues |
2+ 3+ 0 7+ -4 5 17+ -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,2287,33741] |
[a1,a2,a3,a4,a6] |
Generators |
[180:2499:1] |
Generators of the group modulo torsion |
j |
896000/867 |
j-invariant |
L |
4.5046792332897 |
L(r)(E,1)/r! |
Ω |
0.56517224027372 |
Real period |
R |
1.3284089675944 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999992 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
19992m1 119952p1 39984w1 |
Quadratic twists by: -4 -3 -7 |