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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 145794.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
145794.q1 | 145794t2 | \([1, 0, 1, -2003210711, 34509283628546]\) | \(16901491583223625/862488\) | \(45366120363816587301912\) | \([]\) | \(54577152\) | \(3.8207\) | |
145794.q2 | 145794t1 | \([1, 0, 1, -26939906, 38377739414]\) | \(41108661625/11691702\) | \(614973379559918655553398\) | \([]\) | \(18192384\) | \(3.2714\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 145794.q have rank \(0\).
Complex multiplication
The elliptic curves in class 145794.q do not have complex multiplication.Modular form 145794.2.a.q
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.