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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 133952y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 133952.bt1 | 133952y1 | \([0, 1, 0, -757, -19181]\) | \(-2932006912/7750379\) | \(-126982209536\) | \([]\) | \(110592\) | \(0.81815\) | \(\Gamma_0(N)\)-optimal |
| 133952.bt2 | 133952y2 | \([0, 1, 0, 6603, 429779]\) | \(1942951190528/5944921619\) | \(-97401595805696\) | \([]\) | \(331776\) | \(1.3675\) |
Rank
sage: E.rank()
The elliptic curves in class 133952y have rank \(0\).
Complex multiplication
The elliptic curves in class 133952y do not have complex multiplication.Modular form 133952.2.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 Cremona 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 Cremona labels.
