Atkin-Lehner |
2+ 3- 13+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
84474p |
Isogeny class |
Conductor |
84474 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1935360 |
Modular degree for the optimal curve |
Δ |
-7100332563470155776 = -1 · 216 · 311 · 13 · 196 |
Discriminant |
Eigenvalues |
2+ 3- -2 4 4 13+ -2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-63423,128365965] |
[a1,a2,a3,a4,a6] |
Generators |
[-814051630:-11034745065:1685159] |
Generators of the group modulo torsion |
j |
-822656953/207028224 |
j-invariant |
L |
5.2189297678656 |
L(r)(E,1)/r! |
Ω |
0.19211493160705 |
Real period |
R |
13.582832234453 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999930282 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
28158r1 234d1 |
Quadratic twists by: -3 -19 |