Atkin-Lehner |
2- 3+ 5+ 7- |
Signs for the Atkin-Lehner involutions |
Class |
47040en |
Isogeny class |
Conductor |
47040 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
184320 |
Modular degree for the optimal curve |
Δ |
172832486400 = 210 · 39 · 52 · 73 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7- 4 -2 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-183661,-30234035] |
[a1,a2,a3,a4,a6] |
Generators |
[-459634764:-399925:1860867] |
Generators of the group modulo torsion |
j |
1950665639360512/492075 |
j-invariant |
L |
5.2075948704209 |
L(r)(E,1)/r! |
Ω |
0.23061902304591 |
Real period |
R |
11.290471188472 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999989 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
47040cp1 11760bi1 47040hb1 |
Quadratic twists by: -4 8 -7 |