Atkin-Lehner |
2- 3+ 37- 41- |
Signs for the Atkin-Lehner involutions |
Class |
27306f |
Isogeny class |
Conductor |
27306 |
Conductor |
∏ cp |
84 |
Product of Tamagawa factors cp |
deg |
59136 |
Modular degree for the optimal curve |
Δ |
-294270427008 = -1 · 27 · 33 · 373 · 412 |
Discriminant |
Eigenvalues |
2- 3+ -4 -1 -1 -5 -7 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-1592,36155] |
[a1,a2,a3,a4,a6] |
Generators |
[27:97:1] [-45:145:1] |
Generators of the group modulo torsion |
j |
-16517083522563/10898904704 |
j-invariant |
L |
9.2543887357681 |
L(r)(E,1)/r! |
Ω |
0.89783224424109 |
Real period |
R |
0.1227081063084 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999986 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27306a1 |
Quadratic twists by: -3 |