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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 90160.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
90160.y1 | 90160cu4 | \([0, 1, 0, -130795520, -575796317132]\) | \(513516182162686336369/1944885031250\) | \(937221238954112000000\) | \([2]\) | \(17252352\) | \(3.2387\) | |
90160.y2 | 90160cu3 | \([0, 1, 0, -8295520, -8719317132]\) | \(131010595463836369/7704101562500\) | \(3712531844000000000000\) | \([2]\) | \(8626176\) | \(2.8922\) | |
90160.y3 | 90160cu2 | \([0, 1, 0, -2227360, -137772300]\) | \(2535986675931409/1450751712200\) | \(699103183620578508800\) | \([2]\) | \(5750784\) | \(2.6894\) | |
90160.y4 | 90160cu1 | \([0, 1, 0, -1443360, 664102900]\) | \(690080604747409/3406760000\) | \(1641684612055040000\) | \([2]\) | \(2875392\) | \(2.3428\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 90160.y have rank \(0\).
Complex multiplication
The elliptic curves in class 90160.y do not have complex multiplication.Modular form 90160.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.