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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 122010k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
122010.l2 | 122010k1 | \([1, 1, 0, -28592, 1452396]\) | \(21973174804729/4842576900\) | \(569724329708100\) | \([2]\) | \(737280\) | \(1.5448\) | \(\Gamma_0(N)\)-optimal |
122010.l1 | 122010k2 | \([1, 1, 0, -148642, -20852894]\) | \(3087199234101529/199326394890\) | \(23450551032413610\) | \([2]\) | \(1474560\) | \(1.8914\) |
Rank
sage: E.rank()
The elliptic curves in class 122010k have rank \(0\).
Complex multiplication
The elliptic curves in class 122010k do not have complex multiplication.Modular form 122010.2.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 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.