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SageMath
E = EllipticCurve("qn1")
E.isogeny_class()
Elliptic curves in class 369600.qn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
369600.qn1 | 369600qn2 | \([0, 1, 0, -20993, -1175457]\) | \(31226116949/71148\) | \(2331377664000\) | \([2]\) | \(983040\) | \(1.2546\) | |
369600.qn2 | 369600qn1 | \([0, 1, 0, -1793, -4257]\) | \(19465109/11088\) | \(363331584000\) | \([2]\) | \(491520\) | \(0.90804\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 369600.qn have rank \(0\).
Complex multiplication
The elliptic curves in class 369600.qn do not have complex multiplication.Modular form 369600.2.a.qn
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.