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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 381150bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
381150.bs4 | 381150bs1 | \([1, -1, 0, -2641392, 6042948016]\) | \(-100999381393/723148272\) | \(-14592544220714055750000\) | \([2]\) | \(23592960\) | \(2.9361\) | \(\Gamma_0(N)\)-optimal |
381150.bs3 | 381150bs2 | \([1, -1, 0, -68525892, 217861615516]\) | \(1763535241378513/4612311396\) | \(93072694234182417562500\) | \([2, 2]\) | \(47185920\) | \(3.2826\) | |
381150.bs1 | 381150bs3 | \([1, -1, 0, -1095725142, 13960760381266]\) | \(7209828390823479793/49509306\) | \(999057544787804906250\) | \([2]\) | \(94371840\) | \(3.6292\) | |
381150.bs2 | 381150bs4 | \([1, -1, 0, -95478642, 30566955766]\) | \(4770223741048753/2740574865798\) | \(55302572747259228504093750\) | \([2]\) | \(94371840\) | \(3.6292\) |
Rank
sage: E.rank()
The elliptic curves in class 381150bs have rank \(1\).
Complex multiplication
The elliptic curves in class 381150bs do not have complex multiplication.Modular form 381150.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.