Properties

Label 14400.h
Number of curves 2
Conductor 14400
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("14400.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14400.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.h1 14400co1 [0, 0, 0, -480, -3800] [2] 6144 \(\Gamma_0(N)\)-optimal
14400.h2 14400co2 [0, 0, 0, 420, -16400] [2] 12288  

Rank

sage: E.rank()
 

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

Modular form 14400.2.a.h

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

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.