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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 54208.co
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54208.co1 | 54208cg2 | \([0, -1, 0, -1816129, -941431071]\) | \(1426487591593/2156\) | \(1001255211106304\) | \([2]\) | \(737280\) | \(2.1464\) | |
54208.co2 | 54208cg1 | \([0, -1, 0, -112449, -14969887]\) | \(-338608873/13552\) | \(-6293604184096768\) | \([2]\) | \(368640\) | \(1.7998\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54208.co have rank \(1\).
Complex multiplication
The elliptic curves in class 54208.co do not have complex multiplication.Modular form 54208.2.a.co
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.