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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 132878.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
132878.b1 | 132878i2 | \([1, 0, 1, -7587, 217316]\) | \(81182737/12482\) | \(7424584692722\) | \([2]\) | \(280896\) | \(1.1932\) | |
132878.b2 | 132878i1 | \([1, 0, 1, 823, 18840]\) | \(103823/316\) | \(-187964169436\) | \([2]\) | \(140448\) | \(0.84661\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 132878.b have rank \(0\).
Complex multiplication
The elliptic curves in class 132878.b do not have complex multiplication.Modular form 132878.2.a.b
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.