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SageMath
E = EllipticCurve("dw1")
E.isogeny_class()
Elliptic curves in class 288990dw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
288990.dw2 | 288990dw1 | \([1, -1, 1, -2214608, 1274883887]\) | \(-341370886042369/1817528220\) | \(-6395416084566435420\) | \([2]\) | \(8601600\) | \(2.4533\) | \(\Gamma_0(N)\)-optimal |
288990.dw1 | 288990dw2 | \([1, -1, 1, -35478878, 81348634631]\) | \(1403607530712116449/39475350\) | \(138903641525791350\) | \([2]\) | \(17203200\) | \(2.7999\) |
Rank
sage: E.rank()
The elliptic curves in class 288990dw have rank \(1\).
Complex multiplication
The elliptic curves in class 288990dw do not have complex multiplication.Modular form 288990.2.a.dw
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.