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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 284592.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
284592.q1 | 284592q1 | \([0, -1, 0, -1092912, 651109824]\) | \(-3451273/2376\) | \(-99390943967157190656\) | \([]\) | \(8709120\) | \(2.5375\) | \(\Gamma_0(N)\)-optimal |
284592.q2 | 284592q2 | \([0, -1, 0, 8867808, -9731944704]\) | \(1843623047/2044416\) | \(-85520385564629476048896\) | \([]\) | \(26127360\) | \(3.0868\) |
Rank
sage: E.rank()
The elliptic curves in class 284592.q have rank \(1\).
Complex multiplication
The elliptic curves in class 284592.q do not have complex multiplication.Modular form 284592.2.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.