Atkin-Lehner |
2- 3- 7+ 79- |
Signs for the Atkin-Lehner involutions |
Class |
69678x |
Isogeny class |
Conductor |
69678 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
580608 |
Modular degree for the optimal curve |
Δ |
1936227816408312 = 23 · 312 · 78 · 79 |
Discriminant |
Eigenvalues |
2- 3- 0 7+ -3 -4 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-211910,-37434211] |
[a1,a2,a3,a4,a6] |
Generators |
[-2154:2837:8] [-257:177:1] |
Generators of the group modulo torsion |
j |
250417281625/460728 |
j-invariant |
L |
14.771890525807 |
L(r)(E,1)/r! |
Ω |
0.22254090498633 |
Real period |
R |
3.6876842251528 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999726 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23226k1 69678bh1 |
Quadratic twists by: -3 -7 |