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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 234650n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
234650.n2 | 234650n1 | \([1, 0, 1, -293501, -60863352]\) | \(3803721481/26000\) | \(19112389156250000\) | \([2]\) | \(4105728\) | \(1.9581\) | \(\Gamma_0(N)\)-optimal |
234650.n3 | 234650n2 | \([1, 0, 1, -113001, -134868352]\) | \(-217081801/10562500\) | \(-7764408094726562500\) | \([2]\) | \(8211456\) | \(2.3047\) | |
234650.n1 | 234650n3 | \([1, 0, 1, -1872876, 946777898]\) | \(988345570681/44994560\) | \(33075136178240000000\) | \([2]\) | \(12317184\) | \(2.5074\) | |
234650.n4 | 234650n4 | \([1, 0, 1, 1015124, 3603737898]\) | \(157376536199/7722894400\) | \(-5677037045593225000000\) | \([2]\) | \(24634368\) | \(2.8540\) |
Rank
sage: E.rank()
The elliptic curves in class 234650n have rank \(1\).
Complex multiplication
The elliptic curves in class 234650n do not have complex multiplication.Modular form 234650.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.