Atkin-Lehner |
2- 5- 7+ 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
117040cd |
Isogeny class |
Conductor |
117040 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1351680 |
Modular degree for the optimal curve |
Δ |
51860781179863040 = 228 · 5 · 75 · 112 · 19 |
Discriminant |
Eigenvalues |
2- 2 5- 7+ 11- 0 6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-547240,-155249040] |
[a1,a2,a3,a4,a6] |
Generators |
[-2237911364259729418623:-913306127665560610742:5459036897870459541] |
Generators of the group modulo torsion |
j |
4424844982155048361/12661323530240 |
j-invariant |
L |
11.975791107219 |
L(r)(E,1)/r! |
Ω |
0.175561679663 |
Real period |
R |
34.107076025988 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999968159 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
14630k1 |
Quadratic twists by: -4 |