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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 271950.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
271950.be1 | 271950be2 | \([1, 1, 0, -6930616375, -222081073152875]\) | \(58389789169255064704903/621457920000\) | \(391844822979960000000000\) | \([2]\) | \(272498688\) | \(4.0989\) | |
271950.be2 | 271950be1 | \([1, 1, 0, -432824375, -3475856896875]\) | \(-14221861969864791943/46510217625600\) | \(-29325860055436492800000000\) | \([2]\) | \(136249344\) | \(3.7524\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 271950.be have rank \(0\).
Complex multiplication
The elliptic curves in class 271950.be do not have complex multiplication.Modular form 271950.2.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.