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SageMath
E = EllipticCurve("gs1")
E.isogeny_class()
Elliptic curves in class 374850gs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
374850.gs2 | 374850gs1 | \([1, -1, 0, 347058, -15354284]\) | \(3449795831/2071552\) | \(-2776077804528000000\) | \([2]\) | \(7372800\) | \(2.2282\) | \(\Gamma_0(N)\)-optimal |
374850.gs1 | 374850gs2 | \([1, -1, 0, -1416942, -122958284]\) | \(234770924809/130960928\) | \(175500168705004500000\) | \([2]\) | \(14745600\) | \(2.5748\) |
Rank
sage: E.rank()
The elliptic curves in class 374850gs have rank \(0\).
Complex multiplication
The elliptic curves in class 374850gs do not have complex multiplication.Modular form 374850.2.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 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.