Properties

Label 14400dw
Number of curves 4
Conductor 14400
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("14400.dz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14400dw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.dz3 14400dw1 [0, 0, 0, -1200, 11000] [2] 9216 \(\Gamma_0(N)\)-optimal
14400.dz4 14400dw2 [0, 0, 0, 3300, 74000] [2] 18432  
14400.dz1 14400dw3 [0, 0, 0, -37200, -2761000] [2] 27648  
14400.dz2 14400dw4 [0, 0, 0, -32700, -3454000] [2] 55296  

Rank

sage: E.rank()
 

The elliptic curves in class 14400dw have rank \(1\).

Modular form 14400.2.a.dz

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

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.