Atkin-Lehner |
2- 3+ 7- 37- |
Signs for the Atkin-Lehner involutions |
Class |
49728ds |
Isogeny class |
Conductor |
49728 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
-44912738304 = -1 · 217 · 33 · 73 · 37 |
Discriminant |
Eigenvalues |
2- 3+ -1 7- -2 0 -4 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-481,11137] |
[a1,a2,a3,a4,a6] |
Generators |
[-24:91:1] [-3:112:1] |
Generators of the group modulo torsion |
j |
-94091762/342657 |
j-invariant |
L |
8.0486994517288 |
L(r)(E,1)/r! |
Ω |
0.99486983764796 |
Real period |
R |
0.67418362576604 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999993 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
49728bu1 12432p1 |
Quadratic twists by: -4 8 |