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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 6630r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6630.u4 | 6630r1 | \([1, 1, 1, 935, 9047]\) | \(90391899763439/84690294000\) | \(-84690294000\) | \([4]\) | \(8448\) | \(0.78405\) | \(\Gamma_0(N)\)-optimal |
| 6630.u3 | 6630r2 | \([1, 1, 1, -4845, 76095]\) | \(12577973014374481/4642947562500\) | \(4642947562500\) | \([2, 2]\) | \(16896\) | \(1.1306\) | |
| 6630.u2 | 6630r3 | \([1, 1, 1, -33575, -2325733]\) | \(4185743240664514801/113629394531250\) | \(113629394531250\) | \([2]\) | \(33792\) | \(1.4772\) | |
| 6630.u1 | 6630r4 | \([1, 1, 1, -68595, 6884595]\) | \(35694515311673154481/10400566692750\) | \(10400566692750\) | \([2]\) | \(33792\) | \(1.4772\) |
Rank
sage: E.rank()
The elliptic curves in class 6630r have rank \(0\).
Complex multiplication
The elliptic curves in class 6630r do not have complex multiplication.Modular form 6630.2.a.r
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.
