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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 117117.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 117117.bj1 | 117117y1 | \([1, -1, 0, -25128, -979965]\) | \(226981/77\) | \(595262363304609\) | \([2]\) | \(404352\) | \(1.5372\) | \(\Gamma_0(N)\)-optimal |
| 117117.bj2 | 117117y2 | \([1, -1, 0, 73737, -6852546]\) | \(5735339/5929\) | \(-45835201974454893\) | \([2]\) | \(808704\) | \(1.8838\) |
Rank
sage: E.rank()
The elliptic curves in class 117117.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 117117.bj do not have complex multiplication.Modular form 117117.2.a.bj
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.
