Atkin-Lehner |
2+ 3- 7+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
68544bp |
Isogeny class |
Conductor |
68544 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
6.7367203816235E+19 |
Discriminant |
Eigenvalues |
2+ 3- 2 7+ -6 0 17- 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-31780524,-68957669072] |
[a1,a2,a3,a4,a6] |
Generators |
[-293650846506:-12072282880:90518849] |
Generators of the group modulo torsion |
j |
18575453384550358633/352517816448 |
j-invariant |
L |
6.1703443025138 |
L(r)(E,1)/r! |
Ω |
0.063585748183585 |
Real period |
R |
12.129967168804 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999992677 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68544et2 2142q2 22848x2 |
Quadratic twists by: -4 8 -3 |