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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 36784.bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
36784.bk1 | 36784bj3 | \([0, -1, 0, -1489429, -699148899]\) | \(-50357871050752/19\) | \(-137869963264\) | \([]\) | \(291600\) | \(1.9255\) | |
36784.bk2 | 36784bj2 | \([0, -1, 0, -18069, -988579]\) | \(-89915392/6859\) | \(-49771056738304\) | \([]\) | \(97200\) | \(1.3762\) | |
36784.bk3 | 36784bj1 | \([0, -1, 0, 1291, -1219]\) | \(32768/19\) | \(-137869963264\) | \([]\) | \(32400\) | \(0.82692\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 36784.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 36784.bk do not have complex multiplication.Modular form 36784.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.