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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 39984cl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39984.n2 | 39984cl1 | \([0, -1, 0, -2614264, 1830116464]\) | \(-4100379159705193/626805817344\) | \(-302051645868868632576\) | \([2]\) | \(1548288\) | \(2.6589\) | \(\Gamma_0(N)\)-optimal |
39984.n1 | 39984cl2 | \([0, -1, 0, -43256824, 109516643440]\) | \(18575453384550358633/352517816448\) | \(169874917733542920192\) | \([2]\) | \(3096576\) | \(3.0055\) |
Rank
sage: E.rank()
The elliptic curves in class 39984cl have rank \(0\).
Complex multiplication
The elliptic curves in class 39984cl do not have complex multiplication.Modular form 39984.2.a.cl
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.