Atkin-Lehner |
5+ 7+ 13- 47- |
Signs for the Atkin-Lehner involutions |
Class |
21385d |
Isogeny class |
Conductor |
21385 |
Conductor |
∏ cp |
60 |
Product of Tamagawa factors cp |
deg |
695040 |
Modular degree for the optimal curve |
Δ |
-15431048774106875 = -1 · 54 · 72 · 133 · 475 |
Discriminant |
Eigenvalues |
-2 -3 5+ 7+ 3 13- -7 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-542083,-153735876] |
[a1,a2,a3,a4,a6] |
Generators |
[1569:53462:1] |
Generators of the group modulo torsion |
j |
-17616558710080783355904/15431048774106875 |
j-invariant |
L |
1.1901914573268 |
L(r)(E,1)/r! |
Ω |
0.087969130579916 |
Real period |
R |
0.22549414957284 |
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 |
106925n1 |
Quadratic twists by: 5 |