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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 9200.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9200.x1 | 9200e2 | \([0, 0, 0, -875, -7750]\) | \(2315250/529\) | \(16928000000\) | \([2]\) | \(6912\) | \(0.67517\) | |
9200.x2 | 9200e1 | \([0, 0, 0, 125, -750]\) | \(13500/23\) | \(-368000000\) | \([2]\) | \(3456\) | \(0.32860\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9200.x have rank \(0\).
Complex multiplication
The elliptic curves in class 9200.x do not have complex multiplication.Modular form 9200.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.