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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 140790cs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
140790.c2 | 140790cs1 | \([1, 1, 0, 89882, 238152772]\) | \(248858189/76050000\) | \(-24540399416092950000\) | \([2]\) | \(4377600\) | \(2.3997\) | \(\Gamma_0(N)\)-optimal |
140790.c1 | 140790cs2 | \([1, 1, 0, -5260138, 4517098768]\) | \(49880735279731/1523437500\) | \(491594539585195312500\) | \([2]\) | \(8755200\) | \(2.7463\) |
Rank
sage: E.rank()
The elliptic curves in class 140790cs have rank \(1\).
Complex multiplication
The elliptic curves in class 140790cs do not have complex multiplication.Modular form 140790.2.a.cs
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 Cremona 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 Cremona labels.