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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 15606.bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15606.bm1 | 15606bi2 | \([1, -1, 1, -8291, -292247]\) | \(-132651/2\) | \(-950199541254\) | \([]\) | \(31104\) | \(1.1014\) | |
15606.bm2 | 15606bi3 | \([1, -1, 1, -3956, 127959]\) | \(-1167051/512\) | \(-3003099784704\) | \([]\) | \(31104\) | \(1.1014\) | |
15606.bm3 | 15606bi1 | \([1, -1, 1, 379, -2091]\) | \(9261/8\) | \(-5213714904\) | \([]\) | \(10368\) | \(0.55210\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15606.bm have rank \(1\).
Complex multiplication
The elliptic curves in class 15606.bm do not have complex multiplication.Modular form 15606.2.a.bm
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.