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SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 44100.dt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44100.dt1 | 44100cn4 | \([0, 0, 0, -20157375, -34833622250]\) | \(2640279346000/3087\) | \(1059040062108000000\) | \([2]\) | \(1990656\) | \(2.7418\) | |
44100.dt2 | 44100cn3 | \([0, 0, 0, -1249500, -553644875]\) | \(-10061824000/352947\) | \(-7567723777146750000\) | \([2]\) | \(995328\) | \(2.3952\) | |
44100.dt3 | 44100cn2 | \([0, 0, 0, -312375, -21523250]\) | \(9826000/5103\) | \(1750658061852000000\) | \([2]\) | \(663552\) | \(2.1925\) | |
44100.dt4 | 44100cn1 | \([0, 0, 0, 73500, -2615375]\) | \(2048000/1323\) | \(-28367144520750000\) | \([2]\) | \(331776\) | \(1.8459\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 44100.dt have rank \(0\).
Complex multiplication
The elliptic curves in class 44100.dt do not have complex multiplication.Modular form 44100.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.