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Properties

Label 6450.s
Number of curves $2$
Conductor $6450$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6450.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6450.s1 6450n2 [1, 0, 1, -4144401, -3247777052] [2] 241920  
6450.s2 6450n1 [1, 0, 1, -256401, -51841052] [2] 120960 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6450.s have rank \(1\).

Complex multiplication

The elliptic curves in class 6450.s do not have complex multiplication.

Modular form 6450.2.a.s

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{6} + 4q^{7} - q^{8} + q^{9} - 4q^{11} + q^{12} - 4q^{13} - 4q^{14} + q^{16} - 4q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.