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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 166410bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
166410.bf2 | 166410bs1 | \([1, -1, 0, -624384, 127618240]\) | \(5841725401/1857600\) | \(8560329155870529600\) | \([2]\) | \(4257792\) | \(2.3366\) | \(\Gamma_0(N)\)-optimal |
166410.bf1 | 166410bs2 | \([1, -1, 0, -3952584, -2927003720]\) | \(1481933914201/53916840\) | \(248463553749142121640\) | \([2]\) | \(8515584\) | \(2.6832\) |
Rank
sage: E.rank()
The elliptic curves in class 166410bs have rank \(0\).
Complex multiplication
The elliptic curves in class 166410bs do not have complex multiplication.Modular form 166410.2.a.bs
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.