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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 25392.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25392.bi1 | 25392bh2 | \([0, 1, 0, -17656, -908908]\) | \(12214672127/9\) | \(448524288\) | \([2]\) | \(49152\) | \(0.97063\) | |
25392.bi2 | 25392bh1 | \([0, 1, 0, -1096, -14668]\) | \(-2924207/81\) | \(-4036718592\) | \([2]\) | \(24576\) | \(0.62406\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 25392.bi have rank \(0\).
Complex multiplication
The elliptic curves in class 25392.bi do not have complex multiplication.Modular form 25392.2.a.bi
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.