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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 60840y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
60840.cb3 | 60840y1 | \([0, 0, 0, -3042, -59319]\) | \(55296/5\) | \(281499500880\) | \([2]\) | \(73728\) | \(0.93642\) | \(\Gamma_0(N)\)-optimal |
60840.cb2 | 60840y2 | \([0, 0, 0, -10647, 355914]\) | \(148176/25\) | \(22519960070400\) | \([2, 2]\) | \(147456\) | \(1.2830\) | |
60840.cb4 | 60840y3 | \([0, 0, 0, 19773, 2016846]\) | \(237276/625\) | \(-2251996007040000\) | \([2]\) | \(294912\) | \(1.6296\) | |
60840.cb1 | 60840y4 | \([0, 0, 0, -162747, 25269894]\) | \(132304644/5\) | \(18015968056320\) | \([2]\) | \(294912\) | \(1.6296\) |
Rank
sage: E.rank()
The elliptic curves in class 60840y have rank \(1\).
Complex multiplication
The elliptic curves in class 60840y do not have complex multiplication.Modular form 60840.2.a.y
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.