Atkin-Lehner |
2- 3+ 7+ 11- 23- |
Signs for the Atkin-Lehner involutions |
Class |
127512x |
Isogeny class |
Conductor |
127512 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
84480 |
Modular degree for the optimal curve |
Δ |
-2129195376 = -1 · 24 · 33 · 7 · 113 · 232 |
Discriminant |
Eigenvalues |
2- 3+ 1 7+ 11- -7 4 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-507,4923] |
[a1,a2,a3,a4,a6] |
Generators |
[13:-23:1] [9:-33:1] |
Generators of the group modulo torsion |
j |
-33362903808/4928693 |
j-invariant |
L |
12.60279214946 |
L(r)(E,1)/r! |
Ω |
1.4169217131155 |
Real period |
R |
0.3706036367636 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999937333 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
127512a1 |
Quadratic twists by: -3 |