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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 65520a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
65520.n1 | 65520a1 | \([0, 0, 0, -16851483, -25079577318]\) | \(26257105115938658412/1713748278480875\) | \(34541268342107200128000\) | \([2]\) | \(5529600\) | \(3.0746\) | \(\Gamma_0(N)\)-optimal |
65520.n2 | 65520a2 | \([0, 0, 0, 13994397, -106568223102]\) | \(7519085745831768474/126058993542015625\) | \(-5081536859929586784000000\) | \([2]\) | \(11059200\) | \(3.4212\) |
Rank
sage: E.rank()
The elliptic curves in class 65520a have rank \(1\).
Complex multiplication
The elliptic curves in class 65520a do not have complex multiplication.Modular form 65520.2.a.a
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.