Atkin-Lehner |
2+ 3- 7+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
63168z |
Isogeny class |
Conductor |
63168 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
57344 |
Modular degree for the optimal curve |
Δ |
-61890490368 = -1 · 212 · 38 · 72 · 47 |
Discriminant |
Eigenvalues |
2+ 3- -2 7+ -4 -6 2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1449,23895] |
[a1,a2,a3,a4,a6] |
Generators |
[9:-108:1] [-33:192:1] |
Generators of the group modulo torsion |
j |
-82199392192/15109983 |
j-invariant |
L |
10.184175220763 |
L(r)(E,1)/r! |
Ω |
1.0638033418601 |
Real period |
R |
0.59833516802394 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000022 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
63168x1 31584p1 |
Quadratic twists by: -4 8 |