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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 9200.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9200.ba1 | 9200s2 | \([0, 1, 0, -458, 4463]\) | \(-42592000/12167\) | \(-3041750000\) | \([]\) | \(3456\) | \(0.53476\) | |
9200.ba2 | 9200s1 | \([0, 1, 0, 42, -37]\) | \(32000/23\) | \(-5750000\) | \([]\) | \(1152\) | \(-0.014550\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9200.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 9200.ba do not have complex multiplication.Modular form 9200.2.a.ba
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.