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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 117117.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 117117.bn1 | 117117o2 | \([1, -1, 0, -95823792, -360939938423]\) | \(27653883672870015625/6954210586323\) | \(24470085113304208180803\) | \([2]\) | \(15482880\) | \(3.2828\) | |
| 117117.bn2 | 117117o1 | \([1, -1, 0, -5271057, -7041739496]\) | \(-4602875775513625/3426316276383\) | \(-12056329020735432896463\) | \([2]\) | \(7741440\) | \(2.9363\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 117117.bn have rank \(0\).
Complex multiplication
The elliptic curves in class 117117.bn do not have complex multiplication.Modular form 117117.2.a.bn
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.
