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SageMath
E = EllipticCurve("dy1")
E.isogeny_class()
Elliptic curves in class 76608dy
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76608.bg3 | 76608dy1 | \([0, 0, 0, -93036, -6390704]\) | \(466025146777/177366672\) | \(33895298862415872\) | \([2]\) | \(491520\) | \(1.8712\) | \(\Gamma_0(N)\)-optimal |
| 76608.bg2 | 76608dy2 | \([0, 0, 0, -657516, 200660560]\) | \(164503536215257/4178071044\) | \(798441810447826944\) | \([2, 2]\) | \(983040\) | \(2.2178\) | |
| 76608.bg4 | 76608dy3 | \([0, 0, 0, 108564, 640390480]\) | \(740480746823/927484650666\) | \(-177245076936592982016\) | \([2]\) | \(1966080\) | \(2.5643\) | |
| 76608.bg1 | 76608dy4 | \([0, 0, 0, -10455276, 13012211536]\) | \(661397832743623417/443352042\) | \(84725894641876992\) | \([2]\) | \(1966080\) | \(2.5643\) |
Rank
sage: E.rank()
The elliptic curves in class 76608dy have rank \(1\).
Complex multiplication
The elliptic curves in class 76608dy do not have complex multiplication.Modular form 76608.2.a.dy
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.
