Properties

Label 16184d
Number of curves $4$
Conductor $16184$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 16184d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16184.d4 16184d1 \([0, 0, 0, 289, 9826]\) \(432/7\) \(-43254523648\) \([2]\) \(9216\) \(0.72143\) \(\Gamma_0(N)\)-optimal
16184.d3 16184d2 \([0, 0, 0, -5491, 147390]\) \(740772/49\) \(1211126662144\) \([2, 2]\) \(18432\) \(1.0680\)  
16184.d2 16184d3 \([0, 0, 0, -17051, -677994]\) \(11090466/2401\) \(118690412890112\) \([2]\) \(36864\) \(1.4146\)  
16184.d1 16184d4 \([0, 0, 0, -86411, 9776870]\) \(1443468546/7\) \(346036189184\) \([2]\) \(36864\) \(1.4146\)  

Rank

sage: E.rank()
 

The elliptic curves in class 16184d have rank \(1\).

Complex multiplication

The elliptic curves in class 16184d do not have complex multiplication.

Modular form 16184.2.a.d

sage: E.q_eigenform(10)
 
\(q - 2q^{5} + q^{7} - 3q^{9} + 4q^{11} + 2q^{13} + 8q^{19} + O(q^{20})\)  Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.