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SageMath
E = EllipticCurve("dq1")
E.isogeny_class()
Elliptic curves in class 101400.dq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101400.dq1 | 101400bk4 | \([0, 1, 0, -1285808, -547868112]\) | \(3044193988/85293\) | \(6587088320592000000\) | \([2]\) | \(2752512\) | \(2.3900\) | |
| 101400.dq2 | 101400bk2 | \([0, 1, 0, -187308, 18957888]\) | \(37642192/13689\) | \(264296753604000000\) | \([2, 2]\) | \(1376256\) | \(2.0435\) | |
| 101400.dq3 | 101400bk1 | \([0, 1, 0, -166183, 26013638]\) | \(420616192/117\) | \(141184163250000\) | \([2]\) | \(688128\) | \(1.6969\) | \(\Gamma_0(N)\)-optimal |
| 101400.dq4 | 101400bk3 | \([0, 1, 0, 573192, 134553888]\) | \(269676572/257049\) | \(-19851622826256000000\) | \([2]\) | \(2752512\) | \(2.3900\) |
Rank
sage: E.rank()
The elliptic curves in class 101400.dq have rank \(0\).
Complex multiplication
The elliptic curves in class 101400.dq do not have complex multiplication.Modular form 101400.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
