Atkin-Lehner |
2- 5+ 13- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
12220c |
Isogeny class |
Conductor |
12220 |
Conductor |
∏ cp |
30 |
Product of Tamagawa factors cp |
deg |
12960 |
Modular degree for the optimal curve |
Δ |
-111684934400 = -1 · 28 · 52 · 135 · 47 |
Discriminant |
Eigenvalues |
2- -1 5+ 4 -5 13- -3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-221,-16055] |
[a1,a2,a3,a4,a6] |
Generators |
[143:1690:1] |
Generators of the group modulo torsion |
j |
-4684079104/436269275 |
j-invariant |
L |
3.7041411879994 |
L(r)(E,1)/r! |
Ω |
0.4661841082382 |
Real period |
R |
0.26485538814254 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
48880o1 109980z1 61100e1 |
Quadratic twists by: -4 -3 5 |