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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 37026.y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37026.y1 | 37026bm4 | \([1, -1, 1, -1529225006, -23016961247299]\) | \(306234591284035366263793/1727485056\) | \(2230991616750171264\) | \([2]\) | \(10321920\) | \(3.5905\) | |
| 37026.y2 | 37026bm2 | \([1, -1, 1, -95578286, -359608484419]\) | \(74768347616680342513/5615307472896\) | \(7251989737331519668224\) | \([2, 2]\) | \(5160960\) | \(3.2439\) | |
| 37026.y3 | 37026bm3 | \([1, -1, 1, -89305646, -408851217475]\) | \(-60992553706117024753/20624795251201152\) | \(-26636262434109596583900288\) | \([2]\) | \(10321920\) | \(3.5905\) | |
| 37026.y4 | 37026bm1 | \([1, -1, 1, -6367406, -4834656835]\) | \(22106889268753393/4969545596928\) | \(6418008958917496799232\) | \([2]\) | \(2580480\) | \(2.8974\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 37026.y have rank \(1\).
Complex multiplication
The elliptic curves in class 37026.y do not have complex multiplication.Modular form 37026.2.a.y
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
