Properties

Label 14450.a
Number of curves 4
Conductor 14450
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("14450.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14450.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14450.a1 14450g4 [1, 0, 1, -816576, -196331452] [2] 497664  
14450.a2 14450g3 [1, 0, 1, -744326, -247195452] [2] 248832  
14450.a3 14450g2 [1, 0, 1, -310826, 66658548] [2] 165888  
14450.a4 14450g1 [1, 0, 1, -21826, 766548] [2] 82944 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 14450.2.a.a

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.