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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 444360.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
444360.y1 | 444360y4 | \([0, -1, 0, -918520, -318679220]\) | \(282678688658/18600435\) | \(5639233394711992320\) | \([2]\) | \(9732096\) | \(2.3476\) | |
444360.y2 | 444360y2 | \([0, -1, 0, -177920, 22885500]\) | \(4108974916/893025\) | \(135372543768806400\) | \([2, 2]\) | \(4866048\) | \(2.0011\) | |
444360.y3 | 444360y1 | \([0, -1, 0, -167340, 26402292]\) | \(13674725584/945\) | \(35812842266880\) | \([2]\) | \(2433024\) | \(1.6545\) | \(\Gamma_0(N)\)-optimal* |
444360.y4 | 444360y3 | \([0, -1, 0, 393400, 139206252]\) | \(22208984782/40516875\) | \(-12283804897539840000\) | \([2]\) | \(9732096\) | \(2.3476\) |
Rank
sage: E.rank()
The elliptic curves in class 444360.y have rank \(0\).
Complex multiplication
The elliptic curves in class 444360.y do not have complex multiplication.Modular form 444360.2.a.y
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.