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SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 405600.da
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
405600.da1 | 405600da1 | \([0, -1, 0, -60558, 4617612]\) | \(5088448/1053\) | \(5082629877000000\) | \([2]\) | \(2752512\) | \(1.7289\) | \(\Gamma_0(N)\)-optimal |
405600.da2 | 405600da2 | \([0, -1, 0, 129567, 27622737]\) | \(778688/1521\) | \(-469860895296000000\) | \([2]\) | \(5505024\) | \(2.0755\) |
Rank
sage: E.rank()
The elliptic curves in class 405600.da have rank \(0\).
Complex multiplication
The elliptic curves in class 405600.da do not have complex multiplication.Modular form 405600.2.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 LMFDB 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 LMFDB labels.