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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 216384.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
216384.z1 | 216384cs1 | \([0, -1, 0, -91009, -10477151]\) | \(31522396/207\) | \(547435095588864\) | \([2]\) | \(917504\) | \(1.6637\) | \(\Gamma_0(N)\)-optimal |
216384.z2 | 216384cs2 | \([0, -1, 0, -36129, -23044671]\) | \(-986078/42849\) | \(-226638129573789696\) | \([2]\) | \(1835008\) | \(2.0103\) |
Rank
sage: E.rank()
The elliptic curves in class 216384.z have rank \(1\).
Complex multiplication
The elliptic curves in class 216384.z do not have complex multiplication.Modular form 216384.2.a.z
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.