Atkin-Lehner |
2+ 3+ 43- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
97008g |
Isogeny class |
Conductor |
97008 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
31744 |
Modular degree for the optimal curve |
Δ |
-1969650432 = -1 · 28 · 34 · 43 · 472 |
Discriminant |
Eigenvalues |
2+ 3+ 0 0 1 1 -7 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,7,2133] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:45:1] [4:47:1] |
Generators of the group modulo torsion |
j |
128000/7693947 |
j-invariant |
L |
9.9109588404577 |
L(r)(E,1)/r! |
Ω |
1.1674101642417 |
Real period |
R |
2.1224243080561 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000226 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
48504c1 |
Quadratic twists by: -4 |