Atkin-Lehner |
2+ 43- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
129344p |
Isogeny class |
Conductor |
129344 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
64512 |
Modular degree for the optimal curve |
Δ |
15306051584 = 212 · 433 · 47 |
Discriminant |
Eigenvalues |
2+ -2 1 2 -2 -4 -3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-825,-7193] |
[a1,a2,a3,a4,a6] |
Generators |
[-23:12:1] [41:172:1] |
Generators of the group modulo torsion |
j |
15179306176/3736829 |
j-invariant |
L |
9.397814852338 |
L(r)(E,1)/r! |
Ω |
0.90674593135077 |
Real period |
R |
1.7273884789667 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000001433 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
129344l1 64672b1 |
Quadratic twists by: -4 8 |