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SageMath
E = EllipticCurve("gs1")
E.isogeny_class()
Elliptic curves in class 58800.gs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58800.gs1 | 58800ij2 | \([0, 1, 0, -163333, -26097037]\) | \(-102400/3\) | \(-14117880000000000\) | \([]\) | \(396000\) | \(1.8777\) | |
58800.gs2 | 58800ij1 | \([0, 1, 0, 1307, 80723]\) | \(20480/243\) | \(-2927483596800\) | \([]\) | \(79200\) | \(1.0730\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 58800.gs have rank \(0\).
Complex multiplication
The elliptic curves in class 58800.gs do not have complex multiplication.Modular form 58800.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.