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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 494508q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
494508.q2 | 494508q1 | \([0, -1, 0, -384617, 76036710]\) | \(16384/3\) | \(1152156793443304656\) | \([2]\) | \(7526400\) | \(2.1842\) | \(\Gamma_0(N)\)-optimal |
494508.q1 | 494508q2 | \([0, -1, 0, -1826932, -879929672]\) | \(109744/9\) | \(55303526085278623488\) | \([2]\) | \(15052800\) | \(2.5308\) |
Rank
sage: E.rank()
The elliptic curves in class 494508q have rank \(1\).
Complex multiplication
The elliptic curves in class 494508q do not have complex multiplication.Modular form 494508.2.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 Cremona 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 Cremona labels.