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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 9996.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9996.l1 | 9996o1 | \([0, 1, 0, -16529, 811656]\) | \(265327034368/297381\) | \(559785236304\) | \([2]\) | \(17280\) | \(1.1683\) | \(\Gamma_0(N)\)-optimal |
9996.l2 | 9996o2 | \([0, 1, 0, -12364, 1234820]\) | \(-6940769488/18000297\) | \(-542135537088768\) | \([2]\) | \(34560\) | \(1.5149\) |
Rank
sage: E.rank()
The elliptic curves in class 9996.l have rank \(1\).
Complex multiplication
The elliptic curves in class 9996.l do not have complex multiplication.Modular form 9996.2.a.l
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.