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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 103056.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
103056.be1 | 103056f1 | \([0, 1, 0, -6708, -213348]\) | \(130415031250000/262747713\) | \(67263414528\) | \([2]\) | \(126720\) | \(0.96469\) | \(\Gamma_0(N)\)-optimal |
103056.be2 | 103056f2 | \([0, 1, 0, -4448, -357084]\) | \(-9506392154500/47845660977\) | \(-48993956840448\) | \([2]\) | \(253440\) | \(1.3113\) |
Rank
sage: E.rank()
The elliptic curves in class 103056.be have rank \(0\).
Complex multiplication
The elliptic curves in class 103056.be do not have complex multiplication.Modular form 103056.2.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.