Atkin-Lehner |
2+ 3- 11+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
120384z |
Isogeny class |
Conductor |
120384 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
-15277094889357312 = -1 · 215 · 36 · 116 · 192 |
Discriminant |
Eigenvalues |
2+ 3- 2 -2 11+ -2 -6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-303084,64498032] |
[a1,a2,a3,a4,a6] |
Generators |
[276:1368:1] |
Generators of the group modulo torsion |
j |
-128894765196744/639533521 |
j-invariant |
L |
6.7474183884642 |
L(r)(E,1)/r! |
Ω |
0.39553100865563 |
Real period |
R |
2.1323923523577 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000006882 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
120384bk2 60192v2 13376i2 |
Quadratic twists by: -4 8 -3 |