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Properties

Label 436810bx
Number of curves $2$
Conductor $436810$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bx1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 436810bx have rank \(1\).

Complex multiplication

The elliptic curves in class 436810bx do not have complex multiplication.

Modular form 436810.2.a.bx

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - q^{7} + q^{8} - 2 q^{9} + q^{10} - q^{12} + 4 q^{13} - q^{14} - q^{15} + q^{16} - 2 q^{18} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 436810bx

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
436810.bx1 436810bx1 \([1, 1, 1, -219315, -40263695]\) \(-1693700041/32000\) \(-22041559799072000\) \([]\) \(3981312\) \(1.9306\) \(\Gamma_0(N)\)-optimal*
436810.bx2 436810bx2 \([1, 1, 1, 872710, -187468665]\) \(106718863559/83886080\) \(-57780626519679303680\) \([]\) \(11943936\) \(2.4799\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 436810bx1.