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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 463680ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
463680.ba1 | 463680ba1 | \([0, 0, 0, -734508, -237686832]\) | \(8493409990827/185150000\) | \(955333332172800000\) | \([2]\) | \(5898240\) | \(2.2383\) | \(\Gamma_0(N)\)-optimal |
463680.ba2 | 463680ba2 | \([0, 0, 0, 60372, -725107248]\) | \(4716275733/44023437500\) | \(-227151267840000000000\) | \([2]\) | \(11796480\) | \(2.5849\) |
Rank
sage: E.rank()
The elliptic curves in class 463680ba have rank \(0\).
Complex multiplication
The elliptic curves in class 463680ba do not have complex multiplication.Modular form 463680.2.a.ba
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.