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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 414736bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
414736.bb2 | 414736bb1 | \([0, 0, 0, -2980915, 39737981682]\) | \(-3375/784\) | \(-680479074808926297325568\) | \([2]\) | \(30523392\) | \(3.2523\) | \(\Gamma_0(N)\)-optimal* |
414736.bb1 | 414736bb2 | \([0, 0, 0, -193759475, 1028772192434]\) | \(926859375/9604\) | \(8335868666409347142238208\) | \([2]\) | \(61046784\) | \(3.5989\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 414736bb have rank \(0\).
Complex multiplication
The elliptic curves in class 414736bb do not have complex multiplication.Modular form 414736.2.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.