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SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 35280.dl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35280.dl1 | 35280dn2 | \([0, 0, 0, -38367, 2833866]\) | \(10536048/245\) | \(145239779946240\) | \([2]\) | \(110592\) | \(1.5033\) | |
35280.dl2 | 35280dn1 | \([0, 0, 0, -5292, -83349]\) | \(442368/175\) | \(6483918747600\) | \([2]\) | \(55296\) | \(1.1568\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35280.dl have rank \(0\).
Complex multiplication
The elliptic curves in class 35280.dl do not have complex multiplication.Modular form 35280.2.a.dl
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.