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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 238260bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
238260.bc1 | 238260bc1 | \([0, 1, 0, -413465, -101104080]\) | \(10384830939136/159217245\) | \(119848248982685520\) | \([2]\) | \(2903040\) | \(2.0787\) | \(\Gamma_0(N)\)-optimal |
238260.bc2 | 238260bc2 | \([0, 1, 0, -36220, -278258332]\) | \(-436334416/2776779225\) | \(-33442822395551289600\) | \([2]\) | \(5806080\) | \(2.4253\) |
Rank
sage: E.rank()
The elliptic curves in class 238260bc have rank \(0\).
Complex multiplication
The elliptic curves in class 238260bc do not have complex multiplication.Modular form 238260.2.a.bc
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.