Atkin-Lehner |
2- 3+ 5+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
32040f |
Isogeny class |
Conductor |
32040 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
175104 |
Modular degree for the optimal curve |
Δ |
-175178700000000 = -1 · 28 · 39 · 58 · 89 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -4 6 0 6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-64908,-6396732] |
[a1,a2,a3,a4,a6] |
Generators |
[7569:658125:1] |
Generators of the group modulo torsion |
j |
-6001877634048/34765625 |
j-invariant |
L |
4.8848435449967 |
L(r)(E,1)/r! |
Ω |
0.14950117795679 |
Real period |
R |
4.0842851639674 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
64080a1 32040a1 |
Quadratic twists by: -4 -3 |