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Properties

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

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 233450.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
233450.r1 233450r1 \([1, -1, 0, -11492, -465584]\) \(85941272997/1195264\) \(2334500000000\) \([2]\) \(599040\) \(1.1786\) \(\Gamma_0(N)\)-optimal
233450.r2 233450r2 \([1, -1, 0, -1492, -1255584]\) \(-188132517/348792976\) \(-681236281250000\) \([2]\) \(1198080\) \(1.5252\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 233450.2.a.r

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.