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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 369600.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.k1 | 369600k2 | \([0, -1, 0, -38212833, 90933213537]\) | \(12052620205076933/8781696\) | \(4496228352000000000\) | \([2]\) | \(27525120\) | \(2.8903\) | |
| 369600.k2 | 369600k1 | \([0, -1, 0, -2372833, 1440733537]\) | \(-2885728410053/79478784\) | \(-40693137408000000000\) | \([2]\) | \(13762560\) | \(2.5437\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 369600.k have rank \(0\).
Complex multiplication
The elliptic curves in class 369600.k do not have complex multiplication.Modular form 369600.2.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.
