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SageMath
E = EllipticCurve("iz1")
E.isogeny_class()
Elliptic curves in class 270400.iz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
270400.iz1 | 270400iz2 | \([0, -1, 0, -556833, -159738463]\) | \(16974593\) | \(1124864000000000\) | \([2]\) | \(1966080\) | \(1.9502\) | |
270400.iz2 | 270400iz1 | \([0, -1, 0, -36833, -2178463]\) | \(4913\) | \(1124864000000000\) | \([2]\) | \(983040\) | \(1.6037\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 270400.iz have rank \(1\).
Complex multiplication
The elliptic curves in class 270400.iz do not have complex multiplication.Modular form 270400.2.a.iz
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.