Atkin-Lehner |
3- 17+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
40749l |
Isogeny class |
Conductor |
40749 |
Conductor |
∏ cp |
9 |
Product of Tamagawa factors cp |
deg |
15552 |
Modular degree for the optimal curve |
Δ |
-267354189 = -1 · 39 · 172 · 47 |
Discriminant |
Eigenvalues |
-1 3- -1 -4 0 2 17+ -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-261,1782] |
[a1,a2,a3,a4,a6] |
Generators |
[9:-18:1] [-9:63:1] |
Generators of the group modulo torsion |
j |
-6805364401/925101 |
j-invariant |
L |
6.0391238175643 |
L(r)(E,1)/r! |
Ω |
1.687959209067 |
Real period |
R |
0.39752960492325 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
122247p1 40749i1 |
Quadratic twists by: -3 17 |