Properties

Label 14400.f
Number of curves 4
Conductor 14400
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("14400.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14400.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.f1 14400bt3 [0, 0, 0, -29100, 1910000] [2] 32768  
14400.f2 14400bt2 [0, 0, 0, -2100, 20000] [2, 2] 16384  
14400.f3 14400bt1 [0, 0, 0, -975, -11500] [2] 8192 \(\Gamma_0(N)\)-optimal
14400.f4 14400bt4 [0, 0, 0, 6900, 146000] [2] 32768  

Rank

sage: E.rank()
 

The elliptic curves in class 14400.f have rank \(2\).

Modular form 14400.2.a.f

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

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 LMFDB 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 LMFDB labels.