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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 234416bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
234416.bs2 | 234416bs1 | \([0, -1, 0, -365360, -100300864]\) | \(-11192824869409/2563305472\) | \(-1235232053146943488\) | \([2]\) | \(5750784\) | \(2.1912\) | \(\Gamma_0(N)\)-optimal |
234416.bs1 | 234416bs2 | \([0, -1, 0, -6135600, -5847459904]\) | \(53008645999484449/2060047808\) | \(992717064451653632\) | \([2]\) | \(11501568\) | \(2.5378\) |
Rank
sage: E.rank()
The elliptic curves in class 234416bs have rank \(1\).
Complex multiplication
The elliptic curves in class 234416bs do not have complex multiplication.Modular form 234416.2.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.