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SageMath
E = EllipticCurve("dq1")
E.isogeny_class()
Elliptic curves in class 254100.dq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
254100.dq1 | 254100dq1 | \([0, 1, 0, -1710133, -861326512]\) | \(1248870793216/42525\) | \(18833907881250000\) | \([2]\) | \(4032000\) | \(2.2146\) | \(\Gamma_0(N)\)-optimal |
254100.dq2 | 254100dq2 | \([0, 1, 0, -1634508, -940884012]\) | \(-68150496976/14467005\) | \(-102516727379220000000\) | \([2]\) | \(8064000\) | \(2.5611\) |
Rank
sage: E.rank()
The elliptic curves in class 254100.dq have rank \(1\).
Complex multiplication
The elliptic curves in class 254100.dq do not have complex multiplication.Modular form 254100.2.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.