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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 489762y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 489762.y1 | 489762y1 | \([1, -1, 0, -10944296973, -440680325035599]\) | \(41200233490632422261295577/390855326548597092\) | \(1375319741746493680777743012\) | \([2]\) | \(812851200\) | \(4.3697\) | \(\Gamma_0(N)\)-optimal |
| 489762.y2 | 489762y2 | \([1, -1, 0, -10688662503, -462246109066845]\) | \(-38380105394519107097435257/4022272433212893301806\) | \(-14153346029410157490488552532366\) | \([2]\) | \(1625702400\) | \(4.7163\) |
Rank
sage: E.rank()
The elliptic curves in class 489762y have rank \(0\).
Complex multiplication
The elliptic curves in class 489762y do not have complex multiplication.Modular form 489762.2.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 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.
