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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 33810.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33810.d1 | 33810e1 | \([1, 1, 0, -53043, 4598637]\) | \(409014195967/8125440\) | \(327890812462080\) | \([2]\) | \(179200\) | \(1.5771\) | \(\Gamma_0(N)\)-optimal |
33810.d2 | 33810e2 | \([1, 1, 0, 1837, 13719693]\) | \(16974593/2014855200\) | \(-81306674902706400\) | \([2]\) | \(358400\) | \(1.9236\) |
Rank
sage: E.rank()
The elliptic curves in class 33810.d have rank \(0\).
Complex multiplication
The elliptic curves in class 33810.d do not have complex multiplication.Modular form 33810.2.a.d
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.