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Properties

Label 436810.bh
Number of curves $4$
Conductor $436810$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bh1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

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

Complex multiplication

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

Modular form 436810.2.a.bh

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

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 436810.bh

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
436810.bh1 436810bh3 \([1, 1, 0, -54099828, -94369961968]\) \(210103680895849/75449000000\) \(6288270346215693209000000\) \([2]\) \(111974400\) \(3.4592\)  
436810.bh2 436810bh1 \([1, 1, 0, -22867913, 42075547793]\) \(15868125221689/2528900\) \(210770280302520464900\) \([2]\) \(37324800\) \(2.9099\) \(\Gamma_0(N)\)-optimal*
436810.bh3 436810bh2 \([1, 1, 0, -20683863, 50437401623]\) \(-11741970526489/6395335210\) \(-533016961857044003685610\) \([2]\) \(74649600\) \(3.2564\)  
436810.bh4 436810bh4 \([1, 1, 0, 164305172, -664101244968]\) \(5885721311824151/5692551601000\) \(-474443709351627836925841000\) \([2]\) \(223948800\) \(3.8057\)  
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 436810.bh1.