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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 422331bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
422331.bb1 | 422331bb1 | \([0, -1, 1, -3373127, -3053091910]\) | \(-44226936832/16395939\) | \(-1573516685178336593331\) | \([]\) | \(18330624\) | \(2.7774\) | \(\Gamma_0(N)\)-optimal* |
422331.bb2 | 422331bb2 | \([0, -1, 1, 25693183, 30881825015]\) | \(19545301188608/15606257499\) | \(-1497731027656667764622571\) | \([]\) | \(54991872\) | \(3.3267\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 422331bb have rank \(1\).
Complex multiplication
The elliptic curves in class 422331bb do not have complex multiplication.Modular form 422331.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.