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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 130536.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
130536.bs1 | 130536p2 | \([0, 0, 0, -338835, 75718622]\) | \(48986090500/146853\) | \(12897292459226112\) | \([2]\) | \(983040\) | \(1.9606\) | |
130536.bs2 | 130536p1 | \([0, 0, 0, -12495, 2161586]\) | \(-9826000/86247\) | \(-1893650083299072\) | \([2]\) | \(491520\) | \(1.6140\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 130536.bs have rank \(0\).
Complex multiplication
The elliptic curves in class 130536.bs do not have complex multiplication.Modular form 130536.2.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 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.