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SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 333270da
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
333270.da1 | 333270da1 | \([1, -1, 1, -111983, 7981031]\) | \(1439069689/579600\) | \(62549367321747600\) | \([2]\) | \(3244032\) | \(1.9209\) | \(\Gamma_0(N)\)-optimal |
333270.da2 | 333270da2 | \([1, -1, 1, 364117, 57685871]\) | \(49471280711/41992020\) | \(-4531701662460613620\) | \([2]\) | \(6488064\) | \(2.2674\) |
Rank
sage: E.rank()
The elliptic curves in class 333270da have rank \(0\).
Complex multiplication
The elliptic curves in class 333270da do not have complex multiplication.Modular form 333270.2.a.da
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.