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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 221067.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221067.bd1 | 221067bd1 | \([1, -1, 0, -38682, -1132785]\) | \(3723875/1827\) | \(3140510444532153\) | \([2]\) | \(878592\) | \(1.6669\) | \(\Gamma_0(N)\)-optimal |
| 221067.bd2 | 221067bd2 | \([1, -1, 0, 141003, -8787366]\) | \(180362125/123627\) | \(-212507873413342353\) | \([2]\) | \(1757184\) | \(2.0134\) |
Rank
sage: E.rank()
The elliptic curves in class 221067.bd have rank \(1\).
Complex multiplication
The elliptic curves in class 221067.bd do not have complex multiplication.Modular form 221067.2.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.
