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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 259210cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
259210.cc2 | 259210cc1 | \([1, 1, 1, -26461, -62257637]\) | \(-49/40\) | \(-1672658984248454440\) | \([]\) | \(5239080\) | \(2.1758\) | \(\Gamma_0(N)\)-optimal |
259210.cc1 | 259210cc2 | \([1, 1, 1, -12727751, -17483347001]\) | \(-5452947409/250\) | \(-10454118651552840250\) | \([]\) | \(15717240\) | \(2.7251\) |
Rank
sage: E.rank()
The elliptic curves in class 259210cc have rank \(0\).
Complex multiplication
The elliptic curves in class 259210cc do not have complex multiplication.Modular form 259210.2.a.cc
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.