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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 429429bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
429429.bb2 | 429429bb1 | \([1, 0, 0, 60921, -5052296952]\) | \(1/441\) | \(-11027140971552347304663\) | \([2]\) | \(27675648\) | \(2.9084\) | \(\Gamma_0(N)\)-optimal* |
429429.bb1 | 429429bb2 | \([1, 0, 0, -43802184, -109700892861]\) | \(371694959/7203\) | \(180109969202021672642829\) | \([2]\) | \(55351296\) | \(3.2550\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 429429bb have rank \(1\).
Complex multiplication
The elliptic curves in class 429429bb do not have complex multiplication.Modular form 429429.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.