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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 10350bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10350.be2 | 10350bs1 | \([1, -1, 1, -8555, 248447]\) | \(243135625/48668\) | \(13858973437500\) | \([]\) | \(17280\) | \(1.2378\) | \(\Gamma_0(N)\)-optimal |
10350.be1 | 10350bs2 | \([1, -1, 1, -655430, 204402197]\) | \(109348914285625/1472\) | \(419175000000\) | \([3]\) | \(51840\) | \(1.7871\) |
Rank
sage: E.rank()
The elliptic curves in class 10350bs have rank \(0\).
Complex multiplication
The elliptic curves in class 10350bs do not have complex multiplication.Modular form 10350.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.