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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 424830.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
424830.bc1 | 424830bc2 | \([1, 1, 0, -1735017, -1383719931]\) | \(-9966659429209/8489664000\) | \(-492012561258945216000\) | \([]\) | \(26873856\) | \(2.6680\) | |
424830.bc2 | 424830bc1 | \([1, 1, 0, 176718, 31346316]\) | \(10531168151/13384440\) | \(-775685893507290360\) | \([]\) | \(8957952\) | \(2.1187\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 424830.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 424830.bc do not have complex multiplication.Modular form 424830.2.a.bc
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.