Atkin-Lehner |
5+ 11+ 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
12155d |
Isogeny class |
Conductor |
12155 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
4896 |
Modular degree for the optimal curve |
Δ |
-228331675 = -1 · 52 · 11 · 132 · 173 |
Discriminant |
Eigenvalues |
-2 0 5+ -1 11+ 13+ 17- -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-23,728] |
[a1,a2,a3,a4,a6] |
Generators |
[11:-43:1] [8:32:1] |
Generators of the group modulo torsion |
j |
-1345572864/228331675 |
j-invariant |
L |
3.1849758333916 |
L(r)(E,1)/r! |
Ω |
1.4436574555021 |
Real period |
R |
0.18384877366236 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
109395bc1 60775d1 |
Quadratic twists by: -3 5 |