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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 67280y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 67280.o2 | 67280y1 | \([0, 0, 0, -560947, -123066894]\) | \(328509/80\) | \(4753701593372753920\) | \([2]\) | \(1091328\) | \(2.2946\) | \(\Gamma_0(N)\)-optimal |
| 67280.o1 | 67280y2 | \([0, 0, 0, -8365427, -9312061646]\) | \(1089547389/100\) | \(5942126991715942400\) | \([2]\) | \(2182656\) | \(2.6411\) |
Rank
sage: E.rank()
The elliptic curves in class 67280y have rank \(0\).
Complex multiplication
The elliptic curves in class 67280y do not have complex multiplication.Modular form 67280.2.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.
