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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 22736y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22736.j2 | 22736y1 | \([0, -1, 0, 3904, 154624]\) | \(13651919/29696\) | \(-14310214467584\) | \([]\) | \(34560\) | \(1.2085\) | \(\Gamma_0(N)\)-optimal |
| 22736.j1 | 22736y2 | \([0, -1, 0, -356736, -82447616]\) | \(-10418796526321/82044596\) | \(-39536495307997184\) | \([]\) | \(172800\) | \(2.0133\) |
Rank
sage: E.rank()
The elliptic curves in class 22736y have rank \(1\).
Complex multiplication
The elliptic curves in class 22736y do not have complex multiplication.Modular form 22736.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
