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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 250712p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 250712.p2 | 250712p1 | \([0, -1, 0, 1896, 1403228]\) | \(415292/469567\) | \(-851831382105088\) | \([2]\) | \(1105920\) | \(1.5439\) | \(\Gamma_0(N)\)-optimal |
| 250712.p1 | 250712p2 | \([0, -1, 0, -177184, 28121964]\) | \(169556172914/4353013\) | \(15793414273624064\) | \([2]\) | \(2211840\) | \(1.8904\) |
Rank
sage: E.rank()
The elliptic curves in class 250712p have rank \(0\).
Complex multiplication
The elliptic curves in class 250712p do not have complex multiplication.Modular form 250712.2.a.p
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.
