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SageMath
E = EllipticCurve("kk1")
E.isogeny_class()
Elliptic curves in class 277200kk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277200.kk1 | 277200kk1 | \([0, 0, 0, -8370675, -9320380750]\) | \(37537160298467283/5519360000\) | \(9537454080000000000\) | \([2]\) | \(8257536\) | \(2.6561\) | \(\Gamma_0(N)\)-optimal |
277200.kk2 | 277200kk2 | \([0, 0, 0, -7602675, -11099836750]\) | \(-28124139978713043/14526050000000\) | \(-25101014400000000000000\) | \([2]\) | \(16515072\) | \(3.0026\) |
Rank
sage: E.rank()
The elliptic curves in class 277200kk have rank \(1\).
Complex multiplication
The elliptic curves in class 277200kk do not have complex multiplication.Modular form 277200.2.a.kk
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.