Atkin-Lehner |
2- 3+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312cn |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
92160 |
Modular degree for the optimal curve |
Δ |
-4633831094976 = -1 · 26 · 34 · 197 |
Discriminant |
Eigenvalues |
2- 3+ 1 -1 -3 0 -7 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,1685,99529] |
[a1,a2,a3,a4,a6] |
Generators |
[218:3249:8] |
Generators of the group modulo torsion |
j |
175616/1539 |
j-invariant |
L |
4.6537807916302 |
L(r)(E,1)/r! |
Ω |
0.56578160989047 |
Real period |
R |
1.0281751630658 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999990545 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69312dj1 34656o1 3648bd1 |
Quadratic twists by: -4 8 -19 |