Atkin-Lehner |
2+ 5- 7- 31- |
Signs for the Atkin-Lehner involutions |
Class |
69440cb |
Isogeny class |
Conductor |
69440 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
163840 |
Modular degree for the optimal curve |
Δ |
-2430400000000 = -1 · 212 · 58 · 72 · 31 |
Discriminant |
Eigenvalues |
2+ -2 5- 7- 0 2 -8 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-11625,484375] |
[a1,a2,a3,a4,a6] |
Generators |
[50:175:1] [-55:980:1] |
Generators of the group modulo torsion |
j |
-42420912573376/593359375 |
j-invariant |
L |
8.2983345880718 |
L(r)(E,1)/r! |
Ω |
0.81798731297892 |
Real period |
R |
0.63405129092729 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999626 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69440bc1 34720u1 |
Quadratic twists by: -4 8 |