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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 301665.bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
301665.bk1 | 301665bk2 | \([0, 1, 1, -1384335, -627378514]\) | \(-10272454218206642176/682489395\) | \(-19492579610595\) | \([]\) | \(3017088\) | \(2.0069\) | |
301665.bk2 | 301665bk1 | \([0, 1, 1, -15435, -1038319]\) | \(-14239618072576/7905184875\) | \(-225779985214875\) | \([3]\) | \(1005696\) | \(1.4576\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 301665.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 301665.bk do not have complex multiplication.Modular form 301665.2.a.bk
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.