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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 13680.be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13680.be1 | 13680bn2 | \([0, 0, 0, -3358947, -2369478814]\) | \(1403607530712116449/39475350\) | \(117872763494400\) | \([2]\) | \(215040\) | \(2.2105\) | |
13680.be2 | 13680bn1 | \([0, 0, 0, -209667, -37122046]\) | \(-341370886042369/1817528220\) | \(-5427110184468480\) | \([2]\) | \(107520\) | \(1.8640\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13680.be have rank \(0\).
Complex multiplication
The elliptic curves in class 13680.be do not have complex multiplication.Modular form 13680.2.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.