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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 268770.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 268770.bl1 | 268770bl4 | \([1, 1, 1, -183651125, -958016912065]\) | \(28379906689597370652529/1357352437500\) | \(32763188117474437500\) | \([2]\) | \(39813120\) | \(3.2219\) | |
| 268770.bl2 | 268770bl3 | \([1, 1, 1, -11459145, -15024752793]\) | \(-6894246873502147249/47925198774000\) | \(-1156797792246140406000\) | \([2]\) | \(19906560\) | \(2.8754\) | |
| 268770.bl3 | 268770bl2 | \([1, 1, 1, -2465465, -1071786553]\) | \(68663623745397169/19216056254400\) | \(463828883748461553600\) | \([2]\) | \(13271040\) | \(2.6726\) | |
| 268770.bl4 | 268770bl1 | \([1, 1, 1, 401415, -109661625]\) | \(296354077829711/387386634240\) | \(-9350571613645762560\) | \([2]\) | \(6635520\) | \(2.3260\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 268770.bl have rank \(1\).
Complex multiplication
The elliptic curves in class 268770.bl do not have complex multiplication.Modular form 268770.2.a.bl
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
