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SageMath
E = EllipticCurve("gs1")
E.isogeny_class()
Elliptic curves in class 286650.gs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
286650.gs1 | 286650gs2 | \([1, -1, 0, -12607317, -17870587659]\) | \(-397052665540282969/17493884928000\) | \(-9764047867392000000000\) | \([]\) | \(22394880\) | \(2.9845\) | |
286650.gs2 | 286650gs1 | \([1, -1, 0, 788058, -68134284]\) | \(96973777690391/59691453120\) | \(-33316224951555000000\) | \([]\) | \(7464960\) | \(2.4352\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 286650.gs have rank \(0\).
Complex multiplication
The elliptic curves in class 286650.gs do not have complex multiplication.Modular form 286650.2.a.gs
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.