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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 6080.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6080.s1 | 6080m2 | \([0, -1, 0, -81, -79]\) | \(3631696/1805\) | \(29573120\) | \([2]\) | \(2048\) | \(0.12649\) | |
6080.s2 | 6080m1 | \([0, -1, 0, 19, -19]\) | \(702464/475\) | \(-486400\) | \([2]\) | \(1024\) | \(-0.22008\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6080.s have rank \(0\).
Complex multiplication
The elliptic curves in class 6080.s do not have complex multiplication.Modular form 6080.2.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 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.