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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)
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.