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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 9024.bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9024.bk1 | 9024s2 | \([0, 1, 0, -9153, -340065]\) | \(323535264625/59643\) | \(15635054592\) | \([2]\) | \(12288\) | \(0.95870\) | |
9024.bk2 | 9024s1 | \([0, 1, 0, -513, -6561]\) | \(-57066625/34263\) | \(-8981839872\) | \([2]\) | \(6144\) | \(0.61212\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9024.bk have rank \(1\).
Complex multiplication
The elliptic curves in class 9024.bk do not have complex multiplication.Modular form 9024.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.