Properties

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

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Show commands: SageMath
E = EllipticCurve("dw1")
 
E.isogeny_class()
 

Elliptic curves in class 14400.dw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.dw1 14400cw2 \([0, 0, 0, -110700, -14094000]\) \(3721734/25\) \(1007769600000000\) \([2]\) \(73728\) \(1.7136\)  
14400.dw2 14400cw1 \([0, 0, 0, -2700, -486000]\) \(-108/5\) \(-100776960000000\) \([2]\) \(36864\) \(1.3670\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14400.2.a.dw

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