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SageMath
E = EllipticCurve("gs1")
E.isogeny_class()
Elliptic curves in class 424830.gs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 424830.gs1 | 424830gs1 | \([1, 0, 0, -4341, -42435]\) | \(1092727/540\) | \(4470760530180\) | \([2]\) | \(946176\) | \(1.1205\) | \(\Gamma_0(N)\)-optimal |
| 424830.gs2 | 424830gs2 | \([1, 0, 0, 15889, -321609]\) | \(53582633/36450\) | \(-301776335787150\) | \([2]\) | \(1892352\) | \(1.4670\) |
Rank
sage: E.rank()
The elliptic curves in class 424830.gs have rank \(0\).
Complex multiplication
The elliptic curves in class 424830.gs do not have complex multiplication.Modular form 424830.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
