Atkin-Lehner |
2- 3+ 7- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
84084o |
Isogeny class |
Conductor |
84084 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
104832 |
Modular degree for the optimal curve |
Δ |
-4640936332032 = -1 · 28 · 37 · 73 · 11 · 133 |
Discriminant |
Eigenvalues |
2- 3+ 0 7- 11- 13- -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,747,-103599] |
[a1,a2,a3,a4,a6] |
Generators |
[47:182:1] |
Generators of the group modulo torsion |
j |
524288000/52853229 |
j-invariant |
L |
5.2535198853938 |
L(r)(E,1)/r! |
Ω |
0.36667640279228 |
Real period |
R |
0.79596672578866 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000345 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
84084w1 |
Quadratic twists by: -7 |