Atkin-Lehner |
2+ 3- 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312bq |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
345600 |
Modular degree for the optimal curve |
Δ |
-3378062868237504 = -1 · 26 · 310 · 197 |
Discriminant |
Eigenvalues |
2+ 3- -1 3 3 -6 3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,28399,2113401] |
[a1,a2,a3,a4,a6] |
Generators |
[-32:1083:1] |
Generators of the group modulo torsion |
j |
841232384/1121931 |
j-invariant |
L |
8.4487050258471 |
L(r)(E,1)/r! |
Ω |
0.30066849573254 |
Real period |
R |
1.4049867453601 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000965 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69312co1 1083c1 3648f1 |
Quadratic twists by: -4 8 -19 |