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Properties

Label 9450.cf
Number of curves $2$
Conductor $9450$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("cf1")
 
E.isogeny_class()
 

Elliptic curves in class 9450.cf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9450.cf1 9450df2 \([1, -1, 1, -1355, 43647]\) \(-72412707/171500\) \(-651164062500\) \([]\) \(10368\) \(0.95507\)  
9450.cf2 9450df1 \([1, -1, 1, 145, -1353]\) \(804357/2240\) \(-945000000\) \([]\) \(3456\) \(0.40576\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9450.cf have rank \(1\).

Complex multiplication

The elliptic curves in class 9450.cf do not have complex multiplication.

Modular form 9450.2.a.cf

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.