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Properties

Label 9450.ba
Number of curves $2$
Conductor $9450$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 9450.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9450.ba1 9450bz1 \([1, -1, 0, -2742, 58166]\) \(-296595/14\) \(-107641406250\) \([3]\) \(16200\) \(0.87969\) \(\Gamma_0(N)\)-optimal
9450.ba2 9450bz2 \([1, -1, 0, 14133, 142541]\) \(4511445/2744\) \(-189879440625000\) \([]\) \(48600\) \(1.4290\)  

Rank

sage: E.rank()
 

The elliptic curves in class 9450.ba have rank \(0\).

Complex multiplication

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

Modular form 9450.2.a.ba

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{7} - q^{8} - 6 q^{11} + 5 q^{13} - q^{14} + q^{16} - 6 q^{17} + 2 q^{19} + O(q^{20})\) 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.