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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 1320.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1320.k1 | 1320d2 | \([0, 1, 0, -1716, 17424]\) | \(2184181167184/717482205\) | \(183675444480\) | \([2]\) | \(1536\) | \(0.86438\) | |
1320.k2 | 1320d1 | \([0, 1, 0, 309, 2034]\) | \(203269830656/218317275\) | \(-3493076400\) | \([2]\) | \(768\) | \(0.51781\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1320.k have rank \(1\).
Complex multiplication
The elliptic curves in class 1320.k do not have complex multiplication.Modular form 1320.2.a.k
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.