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SageMath
E = EllipticCurve("qz1")
E.isogeny_class()
Elliptic curves in class 1587600.qz
sage: E.isogeny_class().curves
LMFDB label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height |
---|---|---|---|---|---|---|
1587600.qz1 | \([0, 0, 0, -2116800, -1129842000]\) | \(2359296/125\) | \(55576446408000000000\) | \([]\) | \(44789760\) | \(2.5455\) |
1587600.qz2 | \([0, 0, 0, -352800, 80262000]\) | \(884736/5\) | \(27445158720000000\) | \([]\) | \(14929920\) | \(1.9962\) |
Rank
sage: E.rank()
The elliptic curves in class 1587600.qz have rank \(1\).
Complex multiplication
The elliptic curves in class 1587600.qz do not have complex multiplication.Modular form 1587600.2.a.qz
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.