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SageMath
E = EllipticCurve("dq1")
E.isogeny_class()
Elliptic curves in class 354900.dq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
354900.dq1 | 354900dq2 | \([0, 1, 0, -9759468, -11734447932]\) | \(665567485783184/257298363\) | \(39741761734837344000\) | \([2]\) | \(15482880\) | \(2.7261\) | |
354900.dq2 | 354900dq1 | \([0, 1, 0, -519393, -239794632]\) | \(-1605176213504/1640558367\) | \(-15837323781721806000\) | \([2]\) | \(7741440\) | \(2.3796\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 354900.dq have rank \(1\).
Complex multiplication
The elliptic curves in class 354900.dq do not have complex multiplication.Modular form 354900.2.a.dq
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.