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SageMath
E = EllipticCurve("ej1")
E.isogeny_class()
Elliptic curves in class 106560ej
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106560.y1 | 106560ej1 | \([0, 0, 0, -67008, 12756832]\) | \(-2785840267264/4273846875\) | \(-51046553548800000\) | \([]\) | \(829440\) | \(1.8975\) | \(\Gamma_0(N)\)-optimal |
| 106560.y2 | 106560ej2 | \([0, 0, 0, 572352, -256669472]\) | \(1736064508952576/3387451171875\) | \(-40459500000000000000\) | \([]\) | \(2488320\) | \(2.4468\) |
Rank
sage: E.rank()
The elliptic curves in class 106560ej have rank \(1\).
Complex multiplication
The elliptic curves in class 106560ej do not have complex multiplication.Modular form 106560.2.a.ej
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
