Properties

Label 14400.ej
Number of curves $2$
Conductor $14400$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ej1")
 
E.isogeny_class()
 

Elliptic curves in class 14400.ej

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.ej1 14400er2 \([0, 0, 0, -1740, -26800]\) \(195112/9\) \(26873856000\) \([2]\) \(12288\) \(0.76270\)  
14400.ej2 14400er1 \([0, 0, 0, 60, -1600]\) \(64/3\) \(-1119744000\) \([2]\) \(6144\) \(0.41612\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 14400.ej have rank \(0\).

Complex multiplication

The elliptic curves in class 14400.ej do not have complex multiplication.

Modular form 14400.2.a.ej

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

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.