Atkin-Lehner |
2- 11- 17- |
Signs for the Atkin-Lehner involutions |
Class |
8228d |
Isogeny class |
Conductor |
8228 |
Conductor |
∏ cp |
9 |
Product of Tamagawa factors cp |
Δ |
9511568 = 24 · 112 · 173 |
Discriminant |
Eigenvalues |
2- -2 0 -2 11- -5 17- -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-238,1329] |
[a1,a2,a3,a4,a6] |
Generators |
[-12:51:1] [-10:53:1] |
Generators of the group modulo torsion |
j |
773344000/4913 |
j-invariant |
L |
4.1134788839239 |
L(r)(E,1)/r! |
Ω |
2.3141313514155 |
Real period |
R |
0.19750530109077 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999991 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
32912ba2 74052f2 8228c2 |
Quadratic twists by: -4 -3 -11 |