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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 40560be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40560.ck1 | 40560be1 | \([0, 1, 0, -9841095, -10578956400]\) | \(621217777580032/74733890625\) | \(12680247940394609250000\) | \([2]\) | \(2935296\) | \(2.9719\) | \(\Gamma_0(N)\)-optimal |
40560.ck2 | 40560be2 | \([0, 1, 0, 14183100, -54149236452]\) | \(116227003261808/533935546875\) | \(-1449502508046937500000000\) | \([2]\) | \(5870592\) | \(3.3185\) |
Rank
sage: E.rank()
The elliptic curves in class 40560be have rank \(0\).
Complex multiplication
The elliptic curves in class 40560be do not have complex multiplication.Modular form 40560.2.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.