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SageMath
E = EllipticCurve("dw1")
E.isogeny_class()
Elliptic curves in class 79350.dw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
79350.dw1 | 79350dk2 | \([1, 0, 0, -9965313, 5366497617]\) | \(47316161414809/22001657400\) | \(50891170510662946875000\) | \([2]\) | \(8515584\) | \(3.0515\) | |
79350.dw2 | 79350dk1 | \([1, 0, 0, 2201687, 633534617]\) | \(510273943271/370215360\) | \(-856330624047735000000\) | \([2]\) | \(4257792\) | \(2.7049\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 79350.dw have rank \(0\).
Complex multiplication
The elliptic curves in class 79350.dw do not have complex multiplication.Modular form 79350.2.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 LMFDB 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 LMFDB labels.