Properties

Label 14450.bg
Number of curves $4$
Conductor $14450$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 14450.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14450.bg1 14450t4 \([1, 0, 0, -906888, -332495608]\) \(-349938025/8\) \(-1885747578125000\) \([]\) \(151200\) \(2.0445\)  
14450.bg2 14450t3 \([1, 0, 0, -3763, -1048733]\) \(-25/2\) \(-471436894531250\) \([]\) \(50400\) \(1.4952\)  
14450.bg3 14450t1 \([1, 0, 0, -873, 11897]\) \(-121945/32\) \(-19310055200\) \([]\) \(10080\) \(0.69051\) \(\Gamma_0(N)\)-optimal
14450.bg4 14450t2 \([1, 0, 0, 6352, -87808]\) \(46969655/32768\) \(-19773496524800\) \([]\) \(30240\) \(1.2398\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14450.bg have rank \(0\).

Complex multiplication

The elliptic curves in class 14450.bg do not have complex multiplication.

Modular form 14450.2.a.bg

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + 2 q^{7} + q^{8} - 2 q^{9} + 3 q^{11} + q^{12} + 4 q^{13} + 2 q^{14} + q^{16} - 2 q^{18} + 5 q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rrrr} 1 & 3 & 15 & 5 \\ 3 & 1 & 5 & 15 \\ 15 & 5 & 1 & 3 \\ 5 & 15 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.