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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 169338k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
169338.s2 | 169338k1 | \([1, 1, 1, -8538, -379293]\) | \(-14260515625/4382748\) | \(-21154687491132\) | \([2]\) | \(414720\) | \(1.2706\) | \(\Gamma_0(N)\)-optimal |
169338.s1 | 169338k2 | \([1, 1, 1, -145428, -21405597]\) | \(70470585447625/4518018\) | \(21807609944562\) | \([2]\) | \(829440\) | \(1.6171\) |
Rank
sage: E.rank()
The elliptic curves in class 169338k have rank \(0\).
Complex multiplication
The elliptic curves in class 169338k do not have complex multiplication.Modular form 169338.2.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 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.