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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 97344ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97344.y4 | 97344ci1 | \([0, 0, 0, -1900236, -21049193360]\) | \(-822656953/207028224\) | \(-190966470161441872674816\) | \([2]\) | \(10321920\) | \(3.1464\) | \(\Gamma_0(N)\)-optimal |
| 97344.y3 | 97344ci2 | \([0, 0, 0, -126500556, -542626132880]\) | \(242702053576633/2554695936\) | \(2356496403281229983514624\) | \([2, 2]\) | \(20643840\) | \(3.4930\) | |
| 97344.y2 | 97344ci3 | \([0, 0, 0, -227738316, 448653517936]\) | \(1416134368422073/725251155408\) | \(668984404410352640848822272\) | \([2]\) | \(41287680\) | \(3.8396\) | |
| 97344.y1 | 97344ci4 | \([0, 0, 0, -2018867916, -34914829912976]\) | \(986551739719628473/111045168\) | \(102430013414230418522112\) | \([2]\) | \(41287680\) | \(3.8396\) |
Rank
sage: E.rank()
The elliptic curves in class 97344ci have rank \(0\).
Complex multiplication
The elliptic curves in class 97344ci do not have complex multiplication.Modular form 97344.2.a.ci
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.
