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SageMath
E = EllipticCurve("dq1")
E.isogeny_class()
Elliptic curves in class 162240dq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162240.s3 | 162240dq1 | \([0, -1, 0, -10196, -370254]\) | \(379503424/24375\) | \(7529822040000\) | \([2]\) | \(344064\) | \(1.2212\) | \(\Gamma_0(N)\)-optimal |
| 162240.s2 | 162240dq2 | \([0, -1, 0, -31321, 1687321]\) | \(171879616/38025\) | \(751777432473600\) | \([2, 2]\) | \(688128\) | \(1.5678\) | |
| 162240.s1 | 162240dq3 | \([0, -1, 0, -470721, 124455681]\) | \(72929847752/5265\) | \(832738079047680\) | \([2]\) | \(1376256\) | \(1.9144\) | |
| 162240.s4 | 162240dq4 | \([0, -1, 0, 70079, 10265761]\) | \(240641848/428415\) | \(-67760205913620480\) | \([2]\) | \(1376256\) | \(1.9144\) |
Rank
sage: E.rank()
The elliptic curves in class 162240dq have rank \(0\).
Complex multiplication
The elliptic curves in class 162240dq do not have complex multiplication.Modular form 162240.2.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 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.
