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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 132834.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
132834.be1 | 132834i2 | \([1, 0, 0, -24424, -1249288]\) | \(333822098953/53954184\) | \(260426540918856\) | \([]\) | \(1050624\) | \(1.4882\) | |
132834.be2 | 132834i1 | \([1, 0, 0, -6679, 209351]\) | \(6826561273/7074\) | \(34144846866\) | \([]\) | \(350208\) | \(0.93890\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 132834.be have rank \(1\).
Complex multiplication
The elliptic curves in class 132834.be do not have complex multiplication.Modular form 132834.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.