Atkin-Lehner |
2- 3+ 7+ 17- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
40698x |
Isogeny class |
Conductor |
40698 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
258048 |
Modular degree for the optimal curve |
Δ |
171869344432128 = 216 · 33 · 72 · 172 · 193 |
Discriminant |
Eigenvalues |
2- 3+ 2 7+ -4 0 17- 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-122099,-16378925] |
[a1,a2,a3,a4,a6] |
Generators |
[-205:170:1] |
Generators of the group modulo torsion |
j |
7455777422404123539/6365531275264 |
j-invariant |
L |
9.7695563686735 |
L(r)(E,1)/r! |
Ω |
0.25541362747762 |
Real period |
R |
1.1953106791366 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
40698a1 |
Quadratic twists by: -3 |