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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 18480.cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18480.cq1 | 18480dc3 | \([0, 1, 0, -331240, 20678900]\) | \(981281029968144361/522287841796875\) | \(2139291000000000000\) | \([2]\) | \(294912\) | \(2.2086\) | |
| 18480.cq2 | 18480dc2 | \([0, 1, 0, -259960, 50873108]\) | \(474334834335054841/607815140625\) | \(2489610816000000\) | \([2, 2]\) | \(147456\) | \(1.8621\) | |
| 18480.cq3 | 18480dc1 | \([0, 1, 0, -259880, 50906100]\) | \(473897054735271721/779625\) | \(3193344000\) | \([2]\) | \(73728\) | \(1.5155\) | \(\Gamma_0(N)\)-optimal |
| 18480.cq4 | 18480dc4 | \([0, 1, 0, -189960, 78957108]\) | \(-185077034913624841/551466161890875\) | \(-2258805399105024000\) | \([4]\) | \(294912\) | \(2.2086\) |
Rank
sage: E.rank()
The elliptic curves in class 18480.cq have rank \(1\).
Complex multiplication
The elliptic curves in class 18480.cq do not have complex multiplication.Modular form 18480.2.a.cq
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 LMFDB 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 LMFDB labels.
