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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 38646.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38646.p1 | 38646be1 | \([1, -1, 1, -4453952, 2135383395]\) | \(13403946614821979039929/5057590268826067968\) | \(3686983305974203548672\) | \([2]\) | \(5058560\) | \(2.8378\) | \(\Gamma_0(N)\)-optimal |
38646.p2 | 38646be2 | \([1, -1, 1, 13933408, 15227183715]\) | \(410363075617640914325831/374944243169850027552\) | \(-273334353270820670085408\) | \([2]\) | \(10117120\) | \(3.1844\) |
Rank
sage: E.rank()
The elliptic curves in class 38646.p have rank \(0\).
Complex multiplication
The elliptic curves in class 38646.p do not have complex multiplication.Modular form 38646.2.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 LMFDB 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 LMFDB labels.