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SageMath
E = EllipticCurve("dr1")
E.isogeny_class()
Elliptic curves in class 15680.dr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15680.dr1 | 15680ba1 | \([0, 0, 0, -8428, -297808]\) | \(-5154200289/20\) | \(-256901120\) | \([]\) | \(23040\) | \(0.82690\) | \(\Gamma_0(N)\)-optimal |
15680.dr2 | 15680ba2 | \([0, 0, 0, 58772, 2825648]\) | \(1747829720511/1280000000\) | \(-16441671680000000\) | \([]\) | \(161280\) | \(1.7999\) |
Rank
sage: E.rank()
The elliptic curves in class 15680.dr have rank \(0\).
Complex multiplication
The elliptic curves in class 15680.dr do not have complex multiplication.Modular form 15680.2.a.dr
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.