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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 9576u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9576.s4 | 9576u1 | \([0, 0, 0, 2886, 33077]\) | \(227910944768/172414683\) | \(-2011044862512\) | \([4]\) | \(12288\) | \(1.0490\) | \(\Gamma_0(N)\)-optimal |
| 9576.s3 | 9576u2 | \([0, 0, 0, -13359, 283250]\) | \(1412791482832/631868769\) | \(117921877145856\) | \([2, 2]\) | \(24576\) | \(1.3955\) | |
| 9576.s2 | 9576u3 | \([0, 0, 0, -105699, -13032178]\) | \(174947951977348/2957342913\) | \(2207644655182848\) | \([2]\) | \(49152\) | \(1.7421\) | |
| 9576.s1 | 9576u4 | \([0, 0, 0, -180939, 29609750]\) | \(877592260337188/494771571\) | \(369344998665216\) | \([2]\) | \(49152\) | \(1.7421\) |
Rank
sage: E.rank()
The elliptic curves in class 9576u have rank \(0\).
Complex multiplication
The elliptic curves in class 9576u do not have complex multiplication.Modular form 9576.2.a.u
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.
