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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 476850.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
476850.b1 | 476850b1 | \([1, 1, 0, -7400394250, -245004103923500]\) | \(118843307222596927933249/19794099600000000\) | \(7465335076373006250000000000\) | \([2]\) | \(928972800\) | \(4.3562\) | \(\Gamma_0(N)\)-optimal |
476850.b2 | 476850b2 | \([1, 1, 0, -6677894250, -294748951423500]\) | \(-87323024620536113533249/48975797371840020000\) | \(-18471198256137611557990312500000\) | \([2]\) | \(1857945600\) | \(4.7027\) |
Rank
sage: E.rank()
The elliptic curves in class 476850.b have rank \(1\).
Complex multiplication
The elliptic curves in class 476850.b do not have complex multiplication.Modular form 476850.2.a.b
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 LMFDB 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 LMFDB labels.