Atkin-Lehner |
2- 3+ 7- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
69384u |
Isogeny class |
Conductor |
69384 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
483840 |
Modular degree for the optimal curve |
Δ |
-3110282991293184 = -1 · 28 · 36 · 710 · 59 |
Discriminant |
Eigenvalues |
2- 3+ 3 7- -4 0 1 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-106444,-13598108] |
[a1,a2,a3,a4,a6] |
Generators |
[1014:30332:1] |
Generators of the group modulo torsion |
j |
-1844467408/43011 |
j-invariant |
L |
6.7562734755049 |
L(r)(E,1)/r! |
Ω |
0.13197451081752 |
Real period |
R |
6.3992219350437 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999993838 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69384y1 |
Quadratic twists by: -7 |