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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 348726.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
348726.z1 | 348726z1 | \([1, 0, 1, -458991, 119650594]\) | \(1559100313038878875/74219712\) | \(509073004608\) | \([2]\) | \(2611200\) | \(1.7239\) | \(\Gamma_0(N)\)-optimal |
348726.z2 | 348726z2 | \([1, 0, 1, -458231, 120066770]\) | \(-1551368419195022875/10758917283912\) | \(-73795413650352408\) | \([2]\) | \(5222400\) | \(2.0705\) |
Rank
sage: E.rank()
The elliptic curves in class 348726.z have rank \(1\).
Complex multiplication
The elliptic curves in class 348726.z do not have complex multiplication.Modular form 348726.2.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.