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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 8568c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8568.j4 | 8568c1 | \([0, 0, 0, -6359799, -6230596790]\) | \(-152435594466395827792/1646846627220711\) | \(-307341104958437969664\) | \([2]\) | \(276480\) | \(2.7472\) | \(\Gamma_0(N)\)-optimal |
8568.j3 | 8568c2 | \([0, 0, 0, -102019179, -396616526570]\) | \(157304700372188331121828/18069292138401\) | \(13488654304147792896\) | \([2, 2]\) | \(552960\) | \(3.0937\) | |
8568.j1 | 8568c3 | \([0, 0, 0, -1632306819, -25383459170018]\) | \(322159999717985454060440834/4250799\) | \(6346408900608\) | \([2]\) | \(1105920\) | \(3.4403\) | |
8568.j2 | 8568c4 | \([0, 0, 0, -102281619, -394473389042]\) | \(79260902459030376659234/842751810121431609\) | \(1258221710496816420784128\) | \([2]\) | \(1105920\) | \(3.4403\) |
Rank
sage: E.rank()
The elliptic curves in class 8568c have rank \(0\).
Complex multiplication
The elliptic curves in class 8568c do not have complex multiplication.Modular form 8568.2.a.c
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.