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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 57038n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57038.k3 | 57038n1 | \([1, 1, 1, -16794, -844661]\) | \(11134383337/316\) | \(14866498396\) | \([]\) | \(95040\) | \(1.0535\) | \(\Gamma_0(N)\)-optimal |
57038.k2 | 57038n2 | \([1, 1, 1, -29429, 570459]\) | \(59914169497/31554496\) | \(1484509063830976\) | \([]\) | \(285120\) | \(1.6028\) | |
57038.k1 | 57038n3 | \([1, 1, 1, -1883164, 993887229]\) | \(15698803397448457/20709376\) | \(974290838880256\) | \([]\) | \(855360\) | \(2.1521\) |
Rank
sage: E.rank()
The elliptic curves in class 57038n have rank \(1\).
Complex multiplication
The elliptic curves in class 57038n do not have complex multiplication.Modular form 57038.2.a.n
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.