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SageMath
E = EllipticCurve("dn1")
E.isogeny_class()
Elliptic curves in class 98736.dn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
98736.dn1 | 98736bj1 | \([0, 1, 0, -9236, 160092]\) | \(192143824/85833\) | \(38926949200128\) | \([2]\) | \(460800\) | \(1.3032\) | \(\Gamma_0(N)\)-optimal |
98736.dn2 | 98736bj2 | \([0, 1, 0, 31904, 1229732]\) | \(1979654684/1499553\) | \(-2720306802926592\) | \([2]\) | \(921600\) | \(1.6498\) |
Rank
sage: E.rank()
The elliptic curves in class 98736.dn have rank \(0\).
Complex multiplication
The elliptic curves in class 98736.dn do not have complex multiplication.Modular form 98736.2.a.dn
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.