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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 9702s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9702.g2 | 9702s1 | \([1, -1, 0, -1401948, 712131664]\) | \(-10358806345399/1445216256\) | \(-42515053153159200768\) | \([2]\) | \(301056\) | \(2.4978\) | \(\Gamma_0(N)\)-optimal |
9702.g1 | 9702s2 | \([1, -1, 0, -23134428, 42834024400]\) | \(46546832455691959/748268928\) | \(22012410332850182784\) | \([2]\) | \(602112\) | \(2.8444\) |
Rank
sage: E.rank()
The elliptic curves in class 9702s have rank \(1\).
Complex multiplication
The elliptic curves in class 9702s do not have complex multiplication.Modular form 9702.2.a.s
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.