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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 89232bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 89232.y2 | 89232bl1 | \([0, -1, 0, -18477, -39874680]\) | \(-9033613312/8891539371\) | \(-686684196156754224\) | \([2]\) | \(903168\) | \(2.1016\) | \(\Gamma_0(N)\)-optimal |
| 89232.y1 | 89232bl2 | \([0, -1, 0, -1866492, -969795828]\) | \(581972233018192/7558011747\) | \(9339156255366482688\) | \([2]\) | \(1806336\) | \(2.4481\) |
Rank
sage: E.rank()
The elliptic curves in class 89232bl have rank \(1\).
Complex multiplication
The elliptic curves in class 89232bl do not have complex multiplication.Modular form 89232.2.a.bl
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.
