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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 156702.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
156702.u1 | 156702bw1 | \([1, 0, 1, -21145, 9165692]\) | \(-181356420553/6192965376\) | \(-35701212992530176\) | \([3]\) | \(1935360\) | \(1.8565\) | \(\Gamma_0(N)\)-optimal |
156702.u2 | 156702bw2 | \([1, 0, 1, 189800, -243883930]\) | \(131169029575367/4533723856896\) | \(-26136015823957917696\) | \([]\) | \(5806080\) | \(2.4058\) |
Rank
sage: E.rank()
The elliptic curves in class 156702.u have rank \(0\).
Complex multiplication
The elliptic curves in class 156702.u do not have complex multiplication.Modular form 156702.2.a.u
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.