Properties

Label 83790bo
Number of curves $4$
Conductor $83790$
CM no
Rank $2$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 83790bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83790.d3 83790bo1 \([1, -1, 0, -13680, 615600]\) \(3301293169/22800\) \(1955467558800\) \([2]\) \(196608\) \(1.1920\) \(\Gamma_0(N)\)-optimal
83790.d2 83790bo2 \([1, -1, 0, -22500, -268164]\) \(14688124849/8122500\) \(696635317822500\) \([2, 2]\) \(393216\) \(1.5386\)  
83790.d4 83790bo3 \([1, -1, 0, 87750, -2186514]\) \(871257511151/527800050\) \(-45267362952106050\) \([2]\) \(786432\) \(1.8852\)  
83790.d1 83790bo4 \([1, -1, 0, -273870, -55016550]\) \(26487576322129/44531250\) \(3819272575781250\) \([2]\) \(786432\) \(1.8852\)  

Rank

sage: E.rank()
 

The elliptic curves in class 83790bo have rank \(2\).

Complex multiplication

The elliptic curves in class 83790bo do not have complex multiplication.

Modular form 83790.2.a.bo

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 4q^{11} - 2q^{13} + q^{16} + 2q^{17} + q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.