Properties

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

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Show commands for: 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 Torsion structure Modular degree Optimality
16184.d4 16184d1 [0, 0, 0, 289, 9826] [2] 9216 \(\Gamma_0(N)\)-optimal
16184.d3 16184d2 [0, 0, 0, -5491, 147390] [2, 2] 18432  
16184.d2 16184d3 [0, 0, 0, -17051, -677994] [2] 36864  
16184.d1 16184d4 [0, 0, 0, -86411, 9776870] [2] 36864  

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)
 
\( q - 2q^{5} + q^{7} - 3q^{9} + 4q^{11} + 2q^{13} + 8q^{19} + O(q^{20}) \)

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.