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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 4560w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4560.t2 | 4560w1 | \([0, 1, 0, -1256, 59700]\) | \(-53540005609/350208000\) | \(-1434451968000\) | \([2]\) | \(8064\) | \(1.0161\) | \(\Gamma_0(N)\)-optimal |
4560.t1 | 4560w2 | \([0, 1, 0, -31976, 2185524]\) | \(882774443450089/2166000000\) | \(8871936000000\) | \([2]\) | \(16128\) | \(1.3627\) |
Rank
sage: E.rank()
The elliptic curves in class 4560w have rank \(1\).
Complex multiplication
The elliptic curves in class 4560w do not have complex multiplication.Modular form 4560.2.a.w
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.