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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 9576.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9576.d1 | 9576a2 | \([0, 0, 0, -6291, -192050]\) | \(497953800342/17689\) | \(978130944\) | \([2]\) | \(8192\) | \(0.81449\) | |
| 9576.d2 | 9576a1 | \([0, 0, 0, -411, -2714]\) | \(277706124/45619\) | \(1261274112\) | \([2]\) | \(4096\) | \(0.46792\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9576.d have rank \(1\).
Complex multiplication
The elliptic curves in class 9576.d do not have complex multiplication.Modular form 9576.2.a.d
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
