Properties

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

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Show commands: SageMath
E = EllipticCurve("fa1")
 
E.isogeny_class()
 

Elliptic curves in class 14400fa

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.em1 14400fa1 \([0, 0, 0, -300, -2050]\) \(-102400/3\) \(-87480000\) \([]\) \(3840\) \(0.30278\) \(\Gamma_0(N)\)-optimal
14400.em2 14400fa2 \([0, 0, 0, 1500, 98750]\) \(20480/243\) \(-4428675000000\) \([]\) \(19200\) \(1.1075\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14400.2.a.fa

sage: E.q_eigenform(10)
 
\(q + 3 q^{7} - 2 q^{11} - q^{13} - 2 q^{17} - 5 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.