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SageMath
E = EllipticCurve("dq1")
E.isogeny_class()
Elliptic curves in class 88200.dq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88200.dq1 | 88200cb4 | \([0, 0, 0, -2385075, -1416847250]\) | \(546718898/405\) | \(1111528928160000000\) | \([2]\) | \(1769472\) | \(2.3964\) | |
| 88200.dq2 | 88200cb3 | \([0, 0, 0, -1503075, 700834750]\) | \(136835858/1875\) | \(5145967260000000000\) | \([2]\) | \(1769472\) | \(2.3964\) | |
| 88200.dq3 | 88200cb2 | \([0, 0, 0, -180075, -12262250]\) | \(470596/225\) | \(308758035600000000\) | \([2, 2]\) | \(884736\) | \(2.0498\) | |
| 88200.dq4 | 88200cb1 | \([0, 0, 0, 40425, -1457750]\) | \(21296/15\) | \(-5145967260000000\) | \([2]\) | \(442368\) | \(1.7032\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 88200.dq have rank \(1\).
Complex multiplication
The elliptic curves in class 88200.dq do not have complex multiplication.Modular form 88200.2.a.dq
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
