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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 301530v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
301530.v2 | 301530v1 | \([1, 0, 1, -1395249, -597711164]\) | \(2029137179059801/132118594560\) | \(19558293599120163840\) | \([2]\) | \(10137600\) | \(2.4516\) | \(\Gamma_0(N)\)-optimal |
301530.v1 | 301530v2 | \([1, 0, 1, -21962769, -39618410108]\) | \(7914399140778079321/37124373600\) | \(5495739649444130400\) | \([2]\) | \(20275200\) | \(2.7982\) |
Rank
sage: E.rank()
The elliptic curves in class 301530v have rank \(0\).
Complex multiplication
The elliptic curves in class 301530v do not have complex multiplication.Modular form 301530.2.a.v
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.