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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 97104co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97104.ch4 | 97104co1 | \([0, 1, 0, 1927, 11742]\) | \(2048000/1323\) | \(-510944060592\) | \([2]\) | \(124416\) | \(0.93554\) | \(\Gamma_0(N)\)-optimal |
| 97104.ch3 | 97104co2 | \([0, 1, 0, -8188, 88616]\) | \(9826000/5103\) | \(31532547739392\) | \([2]\) | \(248832\) | \(1.2821\) | |
| 97104.ch2 | 97104co3 | \([0, 1, 0, -32753, 2338770]\) | \(-10061824000/352947\) | \(-136308521053488\) | \([2]\) | \(373248\) | \(1.4848\) | |
| 97104.ch1 | 97104co4 | \([0, 1, 0, -528388, 147658952]\) | \(2640279346000/3087\) | \(19075244928768\) | \([2]\) | \(746496\) | \(1.8314\) |
Rank
sage: E.rank()
The elliptic curves in class 97104co have rank \(0\).
Complex multiplication
The elliptic curves in class 97104co do not have complex multiplication.Modular form 97104.2.a.co
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
