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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 73920.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
73920.k1 | 73920eb4 | \([0, -1, 0, -59841, 4067361]\) | \(723231880398728/202569142545\) | \(6637785662914560\) | \([2]\) | \(491520\) | \(1.7431\) | |
73920.k2 | 73920eb2 | \([0, -1, 0, -22041, -1201959]\) | \(289119478354624/13074779025\) | \(53554294886400\) | \([2, 2]\) | \(245760\) | \(1.3965\) | |
73920.k3 | 73920eb1 | \([0, -1, 0, -21796, -1231310]\) | \(17893449053367616/39220335\) | \(2510101440\) | \([2]\) | \(122880\) | \(1.0499\) | \(\Gamma_0(N)\)-optimal |
73920.k4 | 73920eb3 | \([0, -1, 0, 11839, -4596735]\) | \(5599924283512/281331579375\) | \(-9218673192960000\) | \([2]\) | \(491520\) | \(1.7431\) |
Rank
sage: E.rank()
The elliptic curves in class 73920.k have rank \(2\).
Complex multiplication
The elliptic curves in class 73920.k do not have complex multiplication.Modular form 73920.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.