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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 22743m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22743.l2 | 22743m1 | \([1, -1, 0, -683982, -65267937]\) | \(1031831907625/543185433\) | \(18629330549309723817\) | \([2]\) | \(345600\) | \(2.3892\) | \(\Gamma_0(N)\)-optimal |
22743.l1 | 22743m2 | \([1, -1, 0, -6256017, 5975932410]\) | \(789529529265625/7311624327\) | \(250762738035460626423\) | \([2]\) | \(691200\) | \(2.7358\) |
Rank
sage: E.rank()
The elliptic curves in class 22743m have rank \(1\).
Complex multiplication
The elliptic curves in class 22743m do not have complex multiplication.Modular form 22743.2.a.m
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.