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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 48672.bm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48672.bm1 | 48672q1 | \([0, 0, 0, -4414449, 3568903468]\) | \(42246001231552/14414517\) | \(3246143472741019968\) | \([2]\) | \(1032192\) | \(2.5236\) | \(\Gamma_0(N)\)-optimal |
48672.bm2 | 48672q2 | \([0, 0, 0, -3798444, 4600342240]\) | \(-420526439488/390971529\) | \(-5634984461915670810624\) | \([2]\) | \(2064384\) | \(2.8702\) |
Rank
sage: E.rank()
The elliptic curves in class 48672.bm have rank \(0\).
Complex multiplication
The elliptic curves in class 48672.bm do not have complex multiplication.Modular form 48672.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.