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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 439569n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
439569.n2 | 439569n1 | \([1, -1, 1, -155681, 682413320]\) | \(-27/13\) | \(-200912761377879433623\) | \([2]\) | \(11698176\) | \(2.5749\) | \(\Gamma_0(N)\)-optimal* |
439569.n1 | 439569n2 | \([1, -1, 1, -12610136, 17062512536]\) | \(14348907/169\) | \(2611865897912432637099\) | \([2]\) | \(23396352\) | \(2.9215\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 439569n have rank \(1\).
Complex multiplication
The elliptic curves in class 439569n do not have complex multiplication.Modular form 439569.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.