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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 2850.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2850.s1 | 2850v2 | \([1, 1, 1, -19638, 539781]\) | \(428831641421/181752822\) | \(354985980468750\) | \([2]\) | \(13440\) | \(1.4887\) | |
2850.s2 | 2850v1 | \([1, 1, 1, 4112, 64781]\) | \(3936827539/3158028\) | \(-6168023437500\) | \([2]\) | \(6720\) | \(1.1421\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2850.s have rank \(1\).
Complex multiplication
The elliptic curves in class 2850.s do not have complex multiplication.Modular form 2850.2.a.s
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.