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SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 254898.dt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
254898.dt1 | 254898dt2 | \([1, -1, 0, -57384693, -167303478483]\) | \(-843137281012581793/216\) | \(-5353864337304\) | \([]\) | \(15676416\) | \(2.7248\) | |
254898.dt2 | 254898dt1 | \([1, -1, 0, -707373, -230074587]\) | \(-1579268174113/10077696\) | \(-249789894521255424\) | \([]\) | \(5225472\) | \(2.1755\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 254898.dt have rank \(1\).
Complex multiplication
The elliptic curves in class 254898.dt do not have complex multiplication.Modular form 254898.2.a.dt
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.