Properties

Label 14400.cj
Number of curves 8
Conductor 14400
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("14400.cj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14400.cj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.cj1 14400y7 [0, 0, 0, -31104300, 66769598000] [2] 393216  
14400.cj2 14400y5 [0, 0, 0, -1944300, 1042958000] [2, 2] 196608  
14400.cj3 14400y8 [0, 0, 0, -1584300, 1441118000] [2] 393216  
14400.cj4 14400y3 [0, 0, 0, -1152300, -476098000] [2] 98304  
14400.cj5 14400y4 [0, 0, 0, -144300, 9758000] [2, 2] 98304  
14400.cj6 14400y2 [0, 0, 0, -72300, -7378000] [2, 2] 49152  
14400.cj7 14400y1 [0, 0, 0, -300, -322000] [2] 24576 \(\Gamma_0(N)\)-optimal
14400.cj8 14400y6 [0, 0, 0, 503700, 73262000] [2] 196608  

Rank

sage: E.rank()
 

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

Modular form 14400.2.a.cj

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

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.