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Properties

Label 233450.ba
Number of curves $2$
Conductor $233450$
CM no
Rank $0$
Graph

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

Elliptic curves in class 233450.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
233450.ba1 233450ba1 \([1, 0, 1, -9469576, 15206851798]\) \(-240411486219309335065/116641691686510592\) \(-45563160815043200000000\) \([3]\) \(17184960\) \(3.0533\) \(\Gamma_0(N)\)-optimal
233450.ba2 233450ba2 \([1, 0, 1, 74351049, -186416265702]\) \(116365700060754543158135/105775668964829954048\) \(-41318620689386700800000000\) \([]\) \(51554880\) \(3.6026\)  

Rank

sage: E.rank()
 

The elliptic curves in class 233450.ba have rank \(0\).

Complex multiplication

The elliptic curves in class 233450.ba do not have complex multiplication.

Modular form 233450.2.a.ba

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