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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 65520bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
65520.dq1 | 65520bk1 | \([0, 0, 0, -32367, 2238766]\) | \(20093868785104/26374985\) | \(4922205200640\) | \([2]\) | \(184320\) | \(1.3421\) | \(\Gamma_0(N)\)-optimal |
65520.dq2 | 65520bk2 | \([0, 0, 0, -23547, 3485914]\) | \(-1934207124196/5912841025\) | \(-4413912173798400\) | \([2]\) | \(368640\) | \(1.6887\) |
Rank
sage: E.rank()
The elliptic curves in class 65520bk have rank \(0\).
Complex multiplication
The elliptic curves in class 65520bk do not have complex multiplication.Modular form 65520.2.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 Cremona 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 Cremona labels.