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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 32490.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32490.bd1 | 32490bd2 | \([1, -1, 1, -1759943, 890448607]\) | \(651038076963/7220000\) | \(6685749426720060000\) | \([2]\) | \(1382400\) | \(2.4265\) | |
| 32490.bd2 | 32490bd1 | \([1, -1, 1, -200423, -12201569]\) | \(961504803/486400\) | \(450408382431667200\) | \([2]\) | \(691200\) | \(2.0800\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 32490.bd have rank \(1\).
Complex multiplication
The elliptic curves in class 32490.bd do not have complex multiplication.Modular form 32490.2.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.
