Atkin-Lehner |
2+ 3- 5- 13- 47- |
Signs for the Atkin-Lehner involutions |
Class |
18330p |
Isogeny class |
Conductor |
18330 |
Conductor |
∏ cp |
144 |
Product of Tamagawa factors cp |
deg |
161280 |
Modular degree for the optimal curve |
Δ |
-5788023920640000 = -1 · 214 · 39 · 54 · 13 · 472 |
Discriminant |
Eigenvalues |
2+ 3- 5- 2 -4 13- -6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-44803,-5172994] |
[a1,a2,a3,a4,a6] |
Generators |
[490:9272:1] |
Generators of the group modulo torsion |
j |
-9945601718435870761/5788023920640000 |
j-invariant |
L |
4.9424507438012 |
L(r)(E,1)/r! |
Ω |
0.15979620711686 |
Real period |
R |
0.85915868039672 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
54990bl1 91650ca1 |
Quadratic twists by: -3 5 |