Properties

Label 14400.k
Number of curves $4$
Conductor $14400$
CM no
Rank $2$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14400.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.k1 14400bs4 \([0, 0, 0, -194700, 33046000]\) \(546718898/405\) \(604661760000000\) \([2]\) \(98304\) \(1.7700\)  
14400.k2 14400bs3 \([0, 0, 0, -122700, -16346000]\) \(136835858/1875\) \(2799360000000000\) \([2]\) \(98304\) \(1.7700\)  
14400.k3 14400bs2 \([0, 0, 0, -14700, 286000]\) \(470596/225\) \(167961600000000\) \([2, 2]\) \(49152\) \(1.4234\)  
14400.k4 14400bs1 \([0, 0, 0, 3300, 34000]\) \(21296/15\) \(-2799360000000\) \([2]\) \(24576\) \(1.0769\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 14400.k have rank \(2\).

Complex multiplication

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

Modular form 14400.2.a.k

sage: E.q_eigenform(10)
 
\(q - 4q^{7} - 6q^{13} - 2q^{17} - 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.