Properties

Label 1584l
Number of curves 4
Conductor 1584
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1584.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1584l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1584.h3 1584l1 [0, 0, 0, -795, 8138] [2] 768 \(\Gamma_0(N)\)-optimal
1584.h4 1584l2 [0, 0, 0, 645, 34346] [2] 1536  
1584.h1 1584l3 [0, 0, 0, -11595, -478726] [2] 2304  
1584.h2 1584l4 [0, 0, 0, -5835, -954502] [2] 4608  

Rank

sage: E.rank()
 

The elliptic curves in class 1584l have rank \(1\).

Modular form 1584.2.a.h

sage: E.q_eigenform(10)
 
\( q - 2q^{7} - q^{11} - 4q^{13} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.