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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 211600.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 211600.n1 | 211600o3 | \([0, 1, 0, -546633, -155705762]\) | \(488095744/125\) | \(4626121531250000\) | \([2]\) | \(1710720\) | \(1.9918\) | |
| 211600.n2 | 211600o4 | \([0, 1, 0, -480508, -194719512]\) | \(-20720464/15625\) | \(-9252243062500000000\) | \([2]\) | \(3421440\) | \(2.3384\) | |
| 211600.n3 | 211600o1 | \([0, 1, 0, -17633, 613738]\) | \(16384/5\) | \(185044861250000\) | \([2]\) | \(570240\) | \(1.4425\) | \(\Gamma_0(N)\)-optimal |
| 211600.n4 | 211600o2 | \([0, 1, 0, 48492, 4184488]\) | \(21296/25\) | \(-14803588900000000\) | \([2]\) | \(1140480\) | \(1.7891\) |
Rank
sage: E.rank()
The elliptic curves in class 211600.n have rank \(1\).
Complex multiplication
The elliptic curves in class 211600.n do not have complex multiplication.Modular form 211600.2.a.n
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.
