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Properties

Label 34650.bo
Number of curves $2$
Conductor $34650$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bo1")
 
E.isogeny_class()
 

Elliptic curves in class 34650.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
34650.bo1 34650ba2 \([1, -1, 0, -52767, 4678641]\) \(1426487591593/2156\) \(24558187500\) \([2]\) \(98304\) \(1.2617\)  
34650.bo2 34650ba1 \([1, -1, 0, -3267, 75141]\) \(-338608873/13552\) \(-154365750000\) \([2]\) \(49152\) \(0.91514\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 34650.bo have rank \(1\).

Complex multiplication

The elliptic curves in class 34650.bo do not have complex multiplication.

Modular form 34650.2.a.bo

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.