Properties

Label 14400eg
Number of curves $4$
Conductor $14400$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("eg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14400eg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.m4 14400eg1 \([0, 0, 0, 825, 97000]\) \(85184/5625\) \(-4100625000000\) \([2]\) \(24576\) \(1.0998\) \(\Gamma_0(N)\)-optimal
14400.m3 14400eg2 \([0, 0, 0, -27300, 1672000]\) \(48228544/2025\) \(94478400000000\) \([2, 2]\) \(49152\) \(1.4463\)  
14400.m2 14400eg3 \([0, 0, 0, -72300, -5258000]\) \(111980168/32805\) \(12244400640000000\) \([2]\) \(98304\) \(1.7929\)  
14400.m1 14400eg4 \([0, 0, 0, -432300, 109402000]\) \(23937672968/45\) \(16796160000000\) \([2]\) \(98304\) \(1.7929\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14400.2.a.eg

sage: E.q_eigenform(10)
 
\(q - 4q^{7} - 2q^{13} - 6q^{17} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.