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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 348726.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
348726.n1 | 348726n1 | \([1, 0, 1, -366139565, 2696585928680]\) | \(-319620691295711664553/914283853056\) | \(-15527797455744956503296\) | \([3]\) | \(106375680\) | \(3.4889\) | \(\Gamma_0(N)\)-optimal |
348726.n2 | 348726n2 | \([1, 0, 1, -242986220, 4536447641642]\) | \(-93419994408179927833/469406086160449536\) | \(-7972187856135072335555198976\) | \([]\) | \(319127040\) | \(4.0382\) |
Rank
sage: E.rank()
The elliptic curves in class 348726.n have rank \(1\).
Complex multiplication
The elliptic curves in class 348726.n do not have complex multiplication.Modular form 348726.2.a.n
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.