Atkin-Lehner |
3+ 7- 11- 79- |
Signs for the Atkin-Lehner involutions |
Class |
127743o |
Isogeny class |
Conductor |
127743 |
Conductor |
∏ cp |
28 |
Product of Tamagawa factors cp |
deg |
274176 |
Modular degree for the optimal curve |
Δ |
-384943983115923 = -1 · 36 · 73 · 117 · 79 |
Discriminant |
Eigenvalues |
0 3+ 0 7- 11- -1 -2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-24733,1778160] |
[a1,a2,a3,a4,a6] |
Generators |
[-156:1347:1] [-134:1633:1] |
Generators of the group modulo torsion |
j |
-4878401536000000/1122285665061 |
j-invariant |
L |
8.7563318213882 |
L(r)(E,1)/r! |
Ω |
0.51045320119479 |
Real period |
R |
0.61264408909641 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000186 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
127743bk1 |
Quadratic twists by: -7 |