Atkin-Lehner |
2- 3+ 13- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
72384cj |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
9 |
Product of Tamagawa factors cp |
deg |
225792 |
Modular degree for the optimal curve |
Δ |
-59045852508864 = -1 · 26 · 3 · 139 · 29 |
Discriminant |
Eigenvalues |
2- 3+ 3 4 -2 13- -3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,8261,-233339] |
[a1,a2,a3,a4,a6] |
Generators |
[60:689:1] |
Generators of the group modulo torsion |
j |
974067452145152/922591445451 |
j-invariant |
L |
7.8690090946407 |
L(r)(E,1)/r! |
Ω |
0.34159682523787 |
Real period |
R |
2.5595505555519 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000419 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72384ds1 36192q1 |
Quadratic twists by: -4 8 |