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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 111573.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 111573.bd1 | 111573p2 | \([1, -1, 0, -545967, -153929322]\) | \(209849322390625/1882056627\) | \(161416696400133867\) | \([2]\) | \(921600\) | \(2.1247\) | |
| 111573.bd2 | 111573p1 | \([1, -1, 0, -10152, -5722893]\) | \(-1349232625/164333367\) | \(-14094235438459407\) | \([2]\) | \(460800\) | \(1.7782\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 111573.bd have rank \(1\).
Complex multiplication
The elliptic curves in class 111573.bd do not have complex multiplication.Modular form 111573.2.a.bd
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.
