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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 38646x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38646.v1 | 38646x1 | \([1, -1, 1, -3922241, 2990829521]\) | \(9153747013124116391113/5485837418496\) | \(3999175478083584\) | \([2]\) | \(870912\) | \(2.3166\) | \(\Gamma_0(N)\)-optimal |
38646.v2 | 38646x2 | \([1, -1, 1, -3899201, 3027684305]\) | \(-8993380100968273380553/224220843480310272\) | \(-163456994897146188288\) | \([2]\) | \(1741824\) | \(2.6631\) |
Rank
sage: E.rank()
The elliptic curves in class 38646x have rank \(1\).
Complex multiplication
The elliptic curves in class 38646x do not have complex multiplication.Modular form 38646.2.a.x
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.