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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 259182.ct
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
259182.ct1 | 259182ct2 | \([1, -1, 0, -1241961, -532423171]\) | \(8086832279405361/226576\) | \(5935854588048\) | \([2]\) | \(2949120\) | \(1.9617\) | |
259182.ct2 | 259182ct1 | \([1, -1, 0, -77721, -8282323]\) | \(1981858514481/10449152\) | \(273747646884096\) | \([2]\) | \(1474560\) | \(1.6151\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259182.ct have rank \(1\).
Complex multiplication
The elliptic curves in class 259182.ct do not have complex multiplication.Modular form 259182.2.a.ct
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.