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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 1950.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1950.bb1 | 1950y2 | \([1, 0, 0, -227906263, -1324307174983]\) | \(-134057911417971280740025/1872\) | \(-18281250000\) | \([]\) | \(168000\) | \(2.9487\) | |
1950.bb2 | 1950y1 | \([1, 0, 0, -355303, -89334583]\) | \(-198417696411528597145/22989483914821632\) | \(-574737097870540800\) | \([5]\) | \(33600\) | \(2.1440\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1950.bb have rank \(0\).
Complex multiplication
The elliptic curves in class 1950.bb do not have complex multiplication.Modular form 1950.2.a.bb
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.