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SageMath
E = EllipticCurve("gq1")
E.isogeny_class()
Elliptic curves in class 381150gq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 381150.gq3 | 381150gq1 | \([1, -1, 0, -799167, -1306504259]\) | \(-75526045083/943250000\) | \(-704963635277343750000\) | \([2]\) | \(19906560\) | \(2.6821\) | \(\Gamma_0(N)\)-optimal |
| 381150.gq2 | 381150gq2 | \([1, -1, 0, -23486667, -43664066759]\) | \(1917114236485083/7117764500\) | \(5319655591802835937500\) | \([2]\) | \(39813120\) | \(3.0287\) | |
| 381150.gq4 | 381150gq3 | \([1, -1, 0, 7141458, 33899580116]\) | \(73929353373/954060800\) | \(-519808625301873600000000\) | \([2]\) | \(59719680\) | \(3.2315\) | |
| 381150.gq1 | 381150gq4 | \([1, -1, 0, -123538542, 494285220116]\) | \(382704614800227/27778076480\) | \(15134553006054863535000000\) | \([2]\) | \(119439360\) | \(3.5780\) |
Rank
sage: E.rank()
The elliptic curves in class 381150gq have rank \(1\).
Complex multiplication
The elliptic curves in class 381150gq do not have complex multiplication.Modular form 381150.2.a.gq
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
