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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1088c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1088.l4 | 1088c1 | \([0, -1, 0, -193, 705]\) | \(3048625/1088\) | \(285212672\) | \([2]\) | \(384\) | \(0.32333\) | \(\Gamma_0(N)\)-optimal |
| 1088.l3 | 1088c2 | \([0, -1, 0, -2753, 56513]\) | \(8805624625/2312\) | \(606076928\) | \([2]\) | \(768\) | \(0.66990\) | |
| 1088.l2 | 1088c3 | \([0, -1, 0, -6593, -203839]\) | \(120920208625/19652\) | \(5151653888\) | \([2]\) | \(1152\) | \(0.87263\) | |
| 1088.l1 | 1088c4 | \([0, -1, 0, -7233, -161215]\) | \(159661140625/48275138\) | \(12655037775872\) | \([2]\) | \(2304\) | \(1.2192\) |
Rank
sage: E.rank()
The elliptic curves in class 1088c have rank \(1\).
Complex multiplication
The elliptic curves in class 1088c do not have complex multiplication.Modular form 1088.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
