Atkin-Lehner |
2+ 3+ 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
89376j |
Isogeny class |
Conductor |
89376 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
663552 |
Modular degree for the optimal curve |
Δ |
-1298202562577088 = -1 · 26 · 33 · 78 · 194 |
Discriminant |
Eigenvalues |
2+ 3+ -4 7- 2 -6 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-39510,3497796] |
[a1,a2,a3,a4,a6] |
Generators |
[-121:2548:1] [110:686:1] |
Generators of the group modulo torsion |
j |
-905915267776/172414683 |
j-invariant |
L |
7.303801062999 |
L(r)(E,1)/r! |
Ω |
0.46376827873801 |
Real period |
R |
3.9372038782921 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000403 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
89376cz1 12768k1 |
Quadratic twists by: -4 -7 |