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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 282534ce
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
282534.ce2 | 282534ce1 | \([1, 1, 1, -981, 26865]\) | \(-2401/6\) | \(-260926082214\) | \([]\) | \(365400\) | \(0.87852\) | \(\Gamma_0(N)\)-optimal |
282534.ce1 | 282534ce2 | \([1, 1, 1, -135521, -19979233]\) | \(-6329617441/279936\) | \(-12173767291776384\) | \([]\) | \(2557800\) | \(1.8515\) |
Rank
sage: E.rank()
The elliptic curves in class 282534ce have rank \(0\).
Complex multiplication
The elliptic curves in class 282534ce do not have complex multiplication.Modular form 282534.2.a.ce
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.