Atkin-Lehner |
2+ 3+ 7+ 13- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
22386c |
Isogeny class |
Conductor |
22386 |
Conductor |
∏ cp |
28 |
Product of Tamagawa factors cp |
deg |
118272 |
Modular degree for the optimal curve |
Δ |
871338958753536 = 28 · 33 · 72 · 137 · 41 |
Discriminant |
Eigenvalues |
2+ 3+ -1 7+ 1 13- -5 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-60378,-5556204] |
[a1,a2,a3,a4,a6] |
Generators |
[-137:478:1] [-124:270:1] |
Generators of the group modulo torsion |
j |
24342833031142160809/871338958753536 |
j-invariant |
L |
4.8035393857209 |
L(r)(E,1)/r! |
Ω |
0.30523444535235 |
Real period |
R |
0.56204331022801 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
67158bq1 |
Quadratic twists by: -3 |