Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("14400.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14400.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.e1 14400t2 [0, 0, 0, -1260, 17200] [2] 8192  
14400.e2 14400t1 [0, 0, 0, -60, 400] [2] 4096 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 14400.2.a.e

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.