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Properties

Label 431200.bh
Number of curves $2$
Conductor $431200$
CM no
Rank $0$
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 431200.bh have rank \(0\).

Complex multiplication

The elliptic curves in class 431200.bh do not have complex multiplication.

Modular form 431200.2.a.bh

Copy content sage:E.q_eigenform(10)
 
\(q - 2 q^{3} + q^{9} + q^{11} + 2 q^{13} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 431200.bh

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
431200.bh1 431200bh2 \([0, 1, 0, -9281008, 9113614488]\) \(273865201784/47265625\) \(15258707646875000000000\) \([2]\) \(24772608\) \(2.9769\) \(\Gamma_0(N)\)-optimal*
431200.bh2 431200bh1 \([0, 1, 0, 1094742, 813014488]\) \(3595640768/9150625\) \(-369260725054375000000\) \([2]\) \(12386304\) \(2.6303\) \(\Gamma_0(N)\)-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 431200.bh1.