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SageMath
E = EllipticCurve("ds1")
E.isogeny_class()
Elliptic curves in class 155610.ds
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
155610.ds1 | 155610bk1 | \([1, -1, 1, -653, -6159]\) | \(42180533641/726180\) | \(529385220\) | \([2]\) | \(81920\) | \(0.47112\) | \(\Gamma_0(N)\)-optimal |
155610.ds2 | 155610bk2 | \([1, -1, 1, -23, -18003]\) | \(-1771561/192178350\) | \(-140098017150\) | \([2]\) | \(163840\) | \(0.81769\) |
Rank
sage: E.rank()
The elliptic curves in class 155610.ds have rank \(0\).
Complex multiplication
The elliptic curves in class 155610.ds do not have complex multiplication.Modular form 155610.2.a.ds
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.