Atkin-Lehner |
2+ 3+ 13- 19- |
Signs for the Atkin-Lehner involutions |
Class |
84474k |
Isogeny class |
Conductor |
84474 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1048320 |
Modular degree for the optimal curve |
Δ |
-2570231647346688 = -1 · 213 · 33 · 13 · 197 |
Discriminant |
Eigenvalues |
2+ 3+ -2 -5 5 13- 4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-128403,-17844811] |
[a1,a2,a3,a4,a6] |
Generators |
[1373:48229:1] |
Generators of the group modulo torsion |
j |
-184317154371/2023424 |
j-invariant |
L |
3.714716563148 |
L(r)(E,1)/r! |
Ω |
0.12602059199104 |
Real period |
R |
3.684632506108 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000015168 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
84474bn1 4446m1 |
Quadratic twists by: -3 -19 |