Atkin-Lehner |
2+ 3- 7+ 79+ |
Signs for the Atkin-Lehner involutions |
Class |
69678f |
Isogeny class |
Conductor |
69678 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
2370816 |
Modular degree for the optimal curve |
Δ |
169984335048192 = 29 · 36 · 78 · 79 |
Discriminant |
Eigenvalues |
2+ 3- -4 7+ 1 -2 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-5969679,5615520749] |
[a1,a2,a3,a4,a6] |
Generators |
[1409:-827:1] [1213:11962:1] |
Generators of the group modulo torsion |
j |
5598411813720369/40448 |
j-invariant |
L |
5.9488951713038 |
L(r)(E,1)/r! |
Ω |
0.3943468189139 |
Real period |
R |
2.5142399557529 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000134 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7742i1 69678l1 |
Quadratic twists by: -3 -7 |