Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14400.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.g1 14400eh3 \([0, 0, 0, -96300, -11502000]\) \(132304644/5\) \(3732480000000\) \([2]\) \(49152\) \(1.4984\)  
14400.g2 14400eh2 \([0, 0, 0, -6300, -162000]\) \(148176/25\) \(4665600000000\) \([2, 2]\) \(24576\) \(1.1518\)  
14400.g3 14400eh1 \([0, 0, 0, -1800, 27000]\) \(55296/5\) \(58320000000\) \([2]\) \(12288\) \(0.80524\) \(\Gamma_0(N)\)-optimal
14400.g4 14400eh4 \([0, 0, 0, 11700, -918000]\) \(237276/625\) \(-466560000000000\) \([2]\) \(49152\) \(1.4984\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14400.2.a.g

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.