Atkin-Lehner |
2- 3+ 7+ 79+ |
Signs for the Atkin-Lehner involutions |
Class |
69678r |
Isogeny class |
Conductor |
69678 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
175392 |
Modular degree for the optimal curve |
Δ |
-71712141348456 = -1 · 23 · 39 · 78 · 79 |
Discriminant |
Eigenvalues |
2- 3+ 1 7+ -4 4 5 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-4052,-418337] |
[a1,a2,a3,a4,a6] |
j |
-64827/632 |
j-invariant |
L |
4.6933883946741 |
L(r)(E,1)/r! |
Ω |
0.26074379995954 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69678a1 69678t1 |
Quadratic twists by: -3 -7 |