Atkin-Lehner |
2+ 3- 19- 73+ |
Signs for the Atkin-Lehner involutions |
Class |
8322f |
Isogeny class |
Conductor |
8322 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
-34868188383768 = -1 · 23 · 316 · 19 · 732 |
Discriminant |
Eigenvalues |
2+ 3- -4 -4 2 -6 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-9168,440662] |
[a1,a2,a3,a4,a6] |
Generators |
[50:303:1] |
Generators of the group modulo torsion |
j |
-85207815018988921/34868188383768 |
j-invariant |
L |
2.2014758307218 |
L(r)(E,1)/r! |
Ω |
0.61261763645215 |
Real period |
R |
0.44919450970086 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
66576p2 24966p2 |
Quadratic twists by: -4 -3 |