Atkin-Lehner |
2+ 3- 5- 7- 29- |
Signs for the Atkin-Lehner involutions |
Class |
48720w |
Isogeny class |
Conductor |
48720 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
159744 |
Modular degree for the optimal curve |
Δ |
-26981185840560 = -1 · 24 · 34 · 5 · 7 · 296 |
Discriminant |
Eigenvalues |
2+ 3- 5- 7- 0 2 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-73155,-7644312] |
[a1,a2,a3,a4,a6] |
Generators |
[244821876:-13533326586:79507] |
Generators of the group modulo torsion |
j |
-2706086720175794176/1686324115035 |
j-invariant |
L |
8.7224956453123 |
L(r)(E,1)/r! |
Ω |
0.1451415741447 |
Real period |
R |
10.0160776317 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999988 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
24360f1 |
Quadratic twists by: -4 |