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SageMath
E = EllipticCurve("rs1")
E.isogeny_class()
Elliptic curves in class 286650.rs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
286650.rs1 | 286650rs2 | \([1, -1, 1, -28895, 1708557]\) | \(248858189/27378\) | \(293513107592250\) | \([2]\) | \(1572864\) | \(1.5095\) | |
286650.rs2 | 286650rs1 | \([1, -1, 1, -6845, -187743]\) | \(3307949/468\) | \(5017318078500\) | \([2]\) | \(786432\) | \(1.1629\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 286650.rs have rank \(0\).
Complex multiplication
The elliptic curves in class 286650.rs do not have complex multiplication.Modular form 286650.2.a.rs
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.