Properties

Label 159120.bh
Number of curves $6$
Conductor $159120$
CM no
Rank $1$
Graph

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

Elliptic curves in class 159120.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
159120.bh1 159120dz6 \([0, 0, 0, -1750323, -884420782]\) \(397210600760070242/3536192675535\) \(5279507375032350720\) \([2]\) \(2883584\) \(2.4157\)  
159120.bh2 159120dz4 \([0, 0, 0, -189723, 9178778]\) \(1011710313226084/536724738225\) \(400662870186009600\) \([2, 2]\) \(1441792\) \(2.0691\)  
159120.bh3 159120dz2 \([0, 0, 0, -149223, 22163078]\) \(1969080716416336/2472575625\) \(461441953440000\) \([2, 2]\) \(720896\) \(1.7225\)  
159120.bh4 159120dz1 \([0, 0, 0, -149178, 22177127]\) \(31476797652269056/49725\) \(579992400\) \([2]\) \(360448\) \(1.3760\) \(\Gamma_0(N)\)-optimal
159120.bh5 159120dz3 \([0, 0, 0, -109443, 34248242]\) \(-194204905090564/566398828125\) \(-422814459600000000\) \([2]\) \(1441792\) \(2.0691\)  
159120.bh6 159120dz5 \([0, 0, 0, 722877, 71783138]\) \(27980756504588158/17683545112935\) \(-26401391385251051520\) \([2]\) \(2883584\) \(2.4157\)  

Rank

sage: E.rank()
 

The elliptic curves in class 159120.bh have rank \(1\).

Complex multiplication

The elliptic curves in class 159120.bh do not have complex multiplication.

Modular form 159120.2.a.bh

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.