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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 136710s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
136710.gj2 | 136710s1 | \([1, -1, 1, 1093, -203619]\) | \(1685159/209250\) | \(-17946560819250\) | \([]\) | \(362880\) | \(1.2226\) | \(\Gamma_0(N)\)-optimal |
136710.gj1 | 136710s2 | \([1, -1, 1, -230432, -42526389]\) | \(-15777367606441/3574920\) | \(-306607021285320\) | \([]\) | \(1088640\) | \(1.7719\) |
Rank
sage: E.rank()
The elliptic curves in class 136710s have rank \(1\).
Complex multiplication
The elliptic curves in class 136710s do not have complex multiplication.Modular form 136710.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.