Atkin-Lehner |
2- 11+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
8272i |
Isogeny class |
Conductor |
8272 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
4800 |
Modular degree for the optimal curve |
Δ |
-6220544 = -1 · 28 · 11 · 472 |
Discriminant |
Eigenvalues |
2- -1 -1 0 11+ 0 4 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-9581,364177] |
[a1,a2,a3,a4,a6] |
Generators |
[57:-2:1] |
Generators of the group modulo torsion |
j |
-379980749676544/24299 |
j-invariant |
L |
3.1305769097914 |
L(r)(E,1)/r! |
Ω |
1.8027308657447 |
Real period |
R |
0.43414368851146 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2068c1 33088bi1 74448bl1 90992x1 |
Quadratic twists by: -4 8 -3 -11 |