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SageMath
E = EllipticCurve("dk1")
E.isogeny_class()
Elliptic curves in class 158400.dk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
158400.dk1 | 158400hf2 | \([0, 0, 0, -26700, -1670000]\) | \(19034163/121\) | \(13381632000000\) | \([2]\) | \(327680\) | \(1.3557\) | |
158400.dk2 | 158400hf1 | \([0, 0, 0, -2700, 10000]\) | \(19683/11\) | \(1216512000000\) | \([2]\) | \(163840\) | \(1.0092\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 158400.dk have rank \(2\).
Complex multiplication
The elliptic curves in class 158400.dk do not have complex multiplication.Modular form 158400.2.a.dk
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.