Properties

Label 43560.bo
Number of curves $2$
Conductor $43560$
CM no
Rank $0$
Graph

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

Elliptic curves in class 43560.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43560.bo1 43560bm2 \([0, 0, 0, -133947, -18759114]\) \(3721734/25\) \(1785325320345600\) \([2]\) \(268800\) \(1.7612\)  
43560.bo2 43560bm1 \([0, 0, 0, -3267, -646866]\) \(-108/5\) \(-178532532034560\) \([2]\) \(134400\) \(1.4147\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 43560.bo have rank \(0\).

Complex multiplication

The elliptic curves in class 43560.bo do not have complex multiplication.

Modular form 43560.2.a.bo

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