Atkin-Lehner |
2- 3+ 7- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
31164d |
Isogeny class |
Conductor |
31164 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
50688 |
Modular degree for the optimal curve |
Δ |
-100564482816 = -1 · 28 · 32 · 77 · 53 |
Discriminant |
Eigenvalues |
2- 3+ 1 7- 3 0 0 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-42205,3351433] |
[a1,a2,a3,a4,a6] |
Generators |
[103:294:1] |
Generators of the group modulo torsion |
j |
-276056203264/3339 |
j-invariant |
L |
5.1629752499648 |
L(r)(E,1)/r! |
Ω |
0.96644020799044 |
Real period |
R |
0.44518836648126 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
124656dk1 93492w1 4452d1 |
Quadratic twists by: -4 -3 -7 |