Properties

Label 14450bj
Number of curves $2$
Conductor $14450$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bj1")
 
E.isogeny_class()
 

Elliptic curves in class 14450bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14450.y1 14450bj1 \([1, 1, 1, -363, -2819]\) \(-1723025/4\) \(-12282500\) \([]\) \(3840\) \(0.24110\) \(\Gamma_0(N)\)-optimal
14450.y2 14450bj2 \([1, 1, 1, 2612, 44781]\) \(1026895/1024\) \(-1965200000000\) \([]\) \(19200\) \(1.0458\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14450bj have rank \(1\).

Complex multiplication

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

Modular form 14450.2.a.bj

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.