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SageMath
E = EllipticCurve("ed1")
E.isogeny_class()
Elliptic curves in class 254800.ed
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
254800.ed1 | 254800ed2 | \([0, 0, 0, -287875, 57881250]\) | \(5606442/169\) | \(79530724000000000\) | \([2]\) | \(1843200\) | \(2.0193\) | |
254800.ed2 | 254800ed1 | \([0, 0, 0, -42875, -2143750]\) | \(37044/13\) | \(3058874000000000\) | \([2]\) | \(921600\) | \(1.6728\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 254800.ed have rank \(0\).
Complex multiplication
The elliptic curves in class 254800.ed do not have complex multiplication.Modular form 254800.2.a.ed
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.