Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("14400.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14400eh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.g3 14400eh1 [0, 0, 0, -1800, 27000] [2] 12288 \(\Gamma_0(N)\)-optimal
14400.g2 14400eh2 [0, 0, 0, -6300, -162000] [2, 2] 24576  
14400.g1 14400eh3 [0, 0, 0, -96300, -11502000] [2] 49152  
14400.g4 14400eh4 [0, 0, 0, 11700, -918000] [2] 49152  

Rank

sage: E.rank()
 

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

Modular form 14400.2.a.g

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.