Atkin-Lehner |
2+ 3- 5- 89- |
Signs for the Atkin-Lehner involutions |
Class |
128160s |
Isogeny class |
Conductor |
128160 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
112640 |
Modular degree for the optimal curve |
Δ |
-19931443200 = -1 · 212 · 37 · 52 · 89 |
Discriminant |
Eigenvalues |
2+ 3- 5- -2 -2 -4 2 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1272,18736] |
[a1,a2,a3,a4,a6] |
Generators |
[20:-36:1] [-28:180:1] |
Generators of the group modulo torsion |
j |
-76225024/6675 |
j-invariant |
L |
12.382767727195 |
L(r)(E,1)/r! |
Ω |
1.1906546564266 |
Real period |
R |
0.64999786365938 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999989186 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
128160r1 42720k1 |
Quadratic twists by: -4 -3 |