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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 444360be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
444360.be1 | 444360be1 | \([0, -1, 0, -558368140, -4891399774988]\) | \(508017439289666674384/21234429931640625\) | \(804725174358689062500000000\) | \([2]\) | \(227082240\) | \(3.9276\) | \(\Gamma_0(N)\)-optimal |
444360.be2 | 444360be2 | \([0, -1, 0, 268194360, -18137229149988]\) | \(14073614784514581404/945607964406328125\) | \(-143343529632124048599120000000\) | \([2]\) | \(454164480\) | \(4.2742\) |
Rank
sage: E.rank()
The elliptic curves in class 444360be have rank \(0\).
Complex multiplication
The elliptic curves in class 444360be do not have complex multiplication.Modular form 444360.2.a.be
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.