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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 221067.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
221067.be1 | 221067bc2 | \([1, -1, 0, -38682, 2910793]\) | \(4956477625/52983\) | \(68425847401527\) | \([2]\) | \(737280\) | \(1.4705\) | |
221067.be2 | 221067bc1 | \([1, -1, 0, -567, 113152]\) | \(-15625/4263\) | \(-5505527951847\) | \([2]\) | \(368640\) | \(1.1239\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 221067.be have rank \(0\).
Complex multiplication
The elliptic curves in class 221067.be do not have complex multiplication.Modular form 221067.2.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 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.