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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 156702.bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
156702.bk1 | 156702x2 | \([1, 1, 1, -53078957, 148822004435]\) | \(-58547782891689619297/43006704\) | \(-12148329421069296\) | \([]\) | \(11104128\) | \(2.8307\) | |
156702.bk2 | 156702x1 | \([1, 1, 1, -641117, 213165875]\) | \(-103170428183137/9961795584\) | \(-2813960688077500416\) | \([]\) | \(3701376\) | \(2.2814\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 156702.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 156702.bk do not have complex multiplication.Modular form 156702.2.a.bk
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.