Properties

Label 36784.bk
Number of curves $3$
Conductor $36784$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bk1")
 
sage: 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)
 
\(q + 2q^{3} + 3q^{5} - q^{7} + q^{9} + 4q^{13} + 6q^{15} + 3q^{17} + q^{19} + O(q^{20})\)  Toggle raw display

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.