Atkin-Lehner |
2+ 3- 7+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
63168bg |
Isogeny class |
Conductor |
63168 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
442368 |
Modular degree for the optimal curve |
Δ |
-1380185442091008 = -1 · 224 · 36 · 74 · 47 |
Discriminant |
Eigenvalues |
2+ 3- -2 7+ 2 4 -6 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-225729,41242527] |
[a1,a2,a3,a4,a6] |
Generators |
[219:1536:1] |
Generators of the group modulo torsion |
j |
-4852301599161073/5264989632 |
j-invariant |
L |
6.7395381349386 |
L(r)(E,1)/r! |
Ω |
0.47875501166043 |
Real period |
R |
1.1731014072356 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000207 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
63168cq1 1974d1 |
Quadratic twists by: -4 8 |