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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 411840bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
411840.bs2 | 411840bs1 | \([0, 0, 0, -580458828, -5393442568048]\) | \(-113180217375258301213009/260161419375000000\) | \(-49717621482946560000000000\) | \([2]\) | \(123863040\) | \(3.8119\) | \(\Gamma_0(N)\)-optimal* |
411840.bs1 | 411840bs2 | \([0, 0, 0, -9292458828, -344781599368048]\) | \(464352938845529653759213009/2445173327025000\) | \(467279899630298726400000\) | \([2]\) | \(247726080\) | \(4.1585\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 411840bs have rank \(0\).
Complex multiplication
The elliptic curves in class 411840bs do not have complex multiplication.Modular form 411840.2.a.bs
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 Cremona 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 Cremona labels.