Atkin-Lehner |
2- 7+ 11+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
109648f |
Isogeny class |
Conductor |
109648 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
190464 |
Modular degree for the optimal curve |
Δ |
-5189476683776 = -1 · 212 · 76 · 112 · 89 |
Discriminant |
Eigenvalues |
2- 1 -3 7+ 11+ 0 -5 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,1728,-105484] |
[a1,a2,a3,a4,a6] |
Generators |
[76:-686:1] [292:5038:1] |
Generators of the group modulo torsion |
j |
139233463487/1266962081 |
j-invariant |
L |
10.423633430287 |
L(r)(E,1)/r! |
Ω |
0.3786866827869 |
Real period |
R |
3.4407182458767 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999988521 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6853h1 |
Quadratic twists by: -4 |