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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 46800.cy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46800.cy1 | 46800k4 | \([0, 0, 0, -187275, -31193750]\) | \(62275269892/39\) | \(454896000000\) | \([2]\) | \(131072\) | \(1.5571\) | |
| 46800.cy2 | 46800k2 | \([0, 0, 0, -11775, -481250]\) | \(61918288/1521\) | \(4435236000000\) | \([2, 2]\) | \(65536\) | \(1.2106\) | |
| 46800.cy3 | 46800k1 | \([0, 0, 0, -1650, 14875]\) | \(2725888/1053\) | \(191909250000\) | \([2]\) | \(32768\) | \(0.86400\) | \(\Gamma_0(N)\)-optimal |
| 46800.cy4 | 46800k3 | \([0, 0, 0, 1725, -1520750]\) | \(48668/85683\) | \(-999406512000000\) | \([2]\) | \(131072\) | \(1.5571\) |
Rank
sage: E.rank()
The elliptic curves in class 46800.cy have rank \(0\).
Complex multiplication
The elliptic curves in class 46800.cy do not have complex multiplication.Modular form 46800.2.a.cy
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.
