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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 141570.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141570.k1 | 141570dr2 | \([1, -1, 0, -340761735, -719181065795]\) | \(3388383326345613179401/1787816842064922240\) | \(2308908185965578891435730560\) | \([2]\) | \(72253440\) | \(3.9421\) | |
141570.k2 | 141570dr1 | \([1, -1, 0, 80899065, -87786183875]\) | \(45338857965533777399/28814396538470400\) | \(-37212870175498997854617600\) | \([2]\) | \(36126720\) | \(3.5955\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141570.k have rank \(0\).
Complex multiplication
The elliptic curves in class 141570.k do not have complex multiplication.Modular form 141570.2.a.k
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.