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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 82810.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
82810.v1 | 82810f1 | \([1, -1, 0, -280706750, -1665851375980]\) | \(4307585705106105969/381542350192640\) | \(216666169025859769063178240\) | \([2]\) | \(42577920\) | \(3.7935\) | \(\Gamma_0(N)\)-optimal |
82810.v2 | 82810f2 | \([1, -1, 0, 312875330, -7772505098604]\) | \(5964709808210123151/49408483478681600\) | \(-28057558557519025960789145600\) | \([2]\) | \(85155840\) | \(4.1401\) |
Rank
sage: E.rank()
The elliptic curves in class 82810.v have rank \(0\).
Complex multiplication
The elliptic curves in class 82810.v do not have complex multiplication.Modular form 82810.2.a.v
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.