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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 9576.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9576.x1 | 9576z3 | \([0, 0, 0, -25779, -1592642]\) | \(2538016415428/872613\) | \(651402114048\) | \([2]\) | \(16384\) | \(1.2381\) | |
| 9576.x2 | 9576z4 | \([0, 0, 0, -13179, 570022]\) | \(339112345828/8210223\) | \(6128898628608\) | \([2]\) | \(16384\) | \(1.2381\) | |
| 9576.x3 | 9576z2 | \([0, 0, 0, -1839, -17390]\) | \(3685542352/1432809\) | \(267396546816\) | \([2, 2]\) | \(8192\) | \(0.89149\) | |
| 9576.x4 | 9576z1 | \([0, 0, 0, 366, -1955]\) | \(464857088/410571\) | \(-4788900144\) | \([2]\) | \(4096\) | \(0.54492\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9576.x have rank \(0\).
Complex multiplication
The elliptic curves in class 9576.x do not have complex multiplication.Modular form 9576.2.a.x
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
