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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 309442.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
309442.k1 | 309442k2 | \([1, 1, 1, -5721814, 1601439187]\) | \(23342897439572257/12256556974592\) | \(10877739431336623473152\) | \([2]\) | \(24330240\) | \(2.9201\) | |
309442.k2 | 309442k1 | \([1, 1, 1, -3261654, -2250187309]\) | \(4323816191582497/40559181824\) | \(35996423167148294144\) | \([2]\) | \(12165120\) | \(2.5735\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 309442.k have rank \(0\).
Complex multiplication
The elliptic curves in class 309442.k do not have complex multiplication.Modular form 309442.2.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.