Properties

Label 14400.ck
Number of curves $6$
Conductor $14400$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ck1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14400.ck

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.ck1 14400ds5 \([0, 0, 0, -345900, -78302000]\) \(3065617154/9\) \(13436928000000\) \([2]\) \(65536\) \(1.7484\)  
14400.ck2 14400ds4 \([0, 0, 0, -57900, 5362000]\) \(28756228/3\) \(2239488000000\) \([2]\) \(32768\) \(1.4018\)  
14400.ck3 14400ds3 \([0, 0, 0, -21900, -1190000]\) \(1556068/81\) \(60466176000000\) \([2, 2]\) \(32768\) \(1.4018\)  
14400.ck4 14400ds2 \([0, 0, 0, -3900, 70000]\) \(35152/9\) \(1679616000000\) \([2, 2]\) \(16384\) \(1.0552\)  
14400.ck5 14400ds1 \([0, 0, 0, 600, 7000]\) \(2048/3\) \(-34992000000\) \([2]\) \(8192\) \(0.70867\) \(\Gamma_0(N)\)-optimal
14400.ck6 14400ds6 \([0, 0, 0, 14100, -4718000]\) \(207646/6561\) \(-9795520512000000\) \([2]\) \(65536\) \(1.7484\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14400.2.a.ck

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

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.