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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 159120bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
159120.a1 | 159120bc1 | \([0, 0, 0, -40908, -3152113]\) | \(649084058484736/7634149965\) | \(89044725191760\) | \([2]\) | \(737280\) | \(1.4887\) | \(\Gamma_0(N)\)-optimal |
159120.a2 | 159120bc2 | \([0, 0, 0, -8103, -8066302]\) | \(-315278049616/150431501025\) | \(-28074128447289600\) | \([2]\) | \(1474560\) | \(1.8352\) |
Rank
sage: E.rank()
The elliptic curves in class 159120bc have rank \(0\).
Complex multiplication
The elliptic curves in class 159120bc do not have complex multiplication.Modular form 159120.2.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 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.