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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 425880.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
425880.bb1 | 425880bb1 | \([0, 0, 0, -29897283, 29621302958]\) | \(820221748268836/369468094905\) | \(1331265079127577229009920\) | \([2]\) | \(50577408\) | \(3.3243\) | \(\Gamma_0(N)\)-optimal |
425880.bb2 | 425880bb2 | \([0, 0, 0, 103768197, 221805530102]\) | \(17147425715207422/12872524043925\) | \(-92764392791825579421542400\) | \([2]\) | \(101154816\) | \(3.6709\) |
Rank
sage: E.rank()
The elliptic curves in class 425880.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 425880.bb do not have complex multiplication.Modular form 425880.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.