Atkin-Lehner |
2- 3+ 7+ 13- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
99918r |
Isogeny class |
Conductor |
99918 |
Conductor |
∏ cp |
80 |
Product of Tamagawa factors cp |
deg |
568320 |
Modular degree for the optimal curve |
Δ |
1489380918165504 = 220 · 39 · 7 · 132 · 61 |
Discriminant |
Eigenvalues |
2- 3+ -2 7+ 0 13- 4 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-31376,-1054349] |
[a1,a2,a3,a4,a6] |
Generators |
[-143:773:1] |
Generators of the group modulo torsion |
j |
173545026494139/75668389888 |
j-invariant |
L |
8.4290071253255 |
L(r)(E,1)/r! |
Ω |
0.37330525066292 |
Real period |
R |
1.128969802231 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000029744 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
99918b1 |
Quadratic twists by: -3 |