Properties

Label 9450.bu
Number of curves $2$
Conductor $9450$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bu1")
 
E.isogeny_class()
 

Elliptic curves in class 9450.bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9450.bu1 9450v2 \([1, -1, 0, -613242, 184988916]\) \(268691220631875/7529536\) \(714717675000000\) \([3]\) \(77760\) \(1.9525\)  
9450.bu2 9450v1 \([1, -1, 0, -13242, -171084]\) \(24348886875/12845056\) \(135475200000000\) \([]\) \(25920\) \(1.4032\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 9450.2.a.bu

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