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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 84966bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
84966.b2 | 84966bd1 | \([1, 1, 0, -205629, -151712931]\) | \(-68921/672\) | \(-9375572695101011616\) | \([]\) | \(2611200\) | \(2.3227\) | \(\Gamma_0(N)\)-optimal |
84966.b1 | 84966bd2 | \([1, 1, 0, -12242479, 23138628871]\) | \(-14544652121/8168202\) | \(-113960672082246240005706\) | \([]\) | \(13056000\) | \(3.1274\) |
Rank
sage: E.rank()
The elliptic curves in class 84966bd have rank \(0\).
Complex multiplication
The elliptic curves in class 84966bd do not have complex multiplication.Modular form 84966.2.a.bd
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.