Atkin-Lehner |
2+ 3+ 7- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
63168u |
Isogeny class |
Conductor |
63168 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
245760 |
Modular degree for the optimal curve |
Δ |
-80210075516928 = -1 · 216 · 312 · 72 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ -4 7- 2 -4 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-4705,-446879] |
[a1,a2,a3,a4,a6] |
Generators |
[113:672:1] [147:1420:1] |
Generators of the group modulo torsion |
j |
-175798419556/1223908623 |
j-invariant |
L |
7.108328861619 |
L(r)(E,1)/r! |
Ω |
0.25583545032039 |
Real period |
R |
6.9461922230734 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000016 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
63168df1 7896l1 |
Quadratic twists by: -4 8 |