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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 205350.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
205350.k1 | 205350ea1 | \([1, 1, 0, -649334525, 369935080125]\) | \(14910549714397/8599633920\) | \(17462865403811844034560000000\) | \([2]\) | \(165722112\) | \(4.1087\) | \(\Gamma_0(N)\)-optimal |
205350.k2 | 205350ea2 | \([1, 1, 0, 2592457475, 2960126888125]\) | \(948905782000163/550998028800\) | \(-1118885350726655358503400000000\) | \([2]\) | \(331444224\) | \(4.4553\) |
Rank
sage: E.rank()
The elliptic curves in class 205350.k have rank \(0\).
Complex multiplication
The elliptic curves in class 205350.k do not have complex multiplication.Modular form 205350.2.a.k
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.