Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14400.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.l1 14400fi2 \([0, 0, 0, -19380, -1038400]\) \(2156689088/81\) \(30233088000\) \([2]\) \(24576\) \(1.0974\)  
14400.l2 14400fi1 \([0, 0, 0, -1155, -17800]\) \(-29218112/6561\) \(-38263752000\) \([2]\) \(12288\) \(0.75082\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14400.2.a.l

sage: E.q_eigenform(10)
 
\(q - 4q^{7} - 4q^{13} + 8q^{19} + O(q^{20})\)  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.