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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 20160y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20160.q3 | 20160y1 | \([0, 0, 0, -1007688, 389275112]\) | \(151591373397612544/32558203125\) | \(24304568400000000\) | \([2]\) | \(245760\) | \(2.1390\) | \(\Gamma_0(N)\)-optimal |
| 20160.q2 | 20160y2 | \([0, 0, 0, -1120188, 296980112]\) | \(13015144447800784/4341909875625\) | \(51859493672232960000\) | \([2, 2]\) | \(491520\) | \(2.4855\) | |
| 20160.q1 | 20160y3 | \([0, 0, 0, -7294188, -7361249488]\) | \(898353183174324196/29899176238575\) | \(1428455389785042124800\) | \([2]\) | \(983040\) | \(2.8321\) | |
| 20160.q4 | 20160y4 | \([0, 0, 0, 3253812, 2048329712]\) | \(79743193254623804/84085819746075\) | \(-4017262598218624204800\) | \([2]\) | \(983040\) | \(2.8321\) |
Rank
sage: E.rank()
The elliptic curves in class 20160y have rank \(0\).
Complex multiplication
The elliptic curves in class 20160y do not have complex multiplication.Modular form 20160.2.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.
