Properties

Label 44880.bh
Number of curves $8$
Conductor $44880$
CM no
Rank $1$
Graph

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

Elliptic curves in class 44880.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44880.bh1 44880br8 \([0, -1, 0, -3219783720, 70322579406960]\) \(901247067798311192691198986281/552431869440\) \(2262760937226240\) \([2]\) \(15925248\) \(3.6539\)  
44880.bh2 44880br7 \([0, -1, 0, -202588200, 1083331543152]\) \(224494757451893010998773801/6152490825146276160000\) \(25200602419799147151360000\) \([2]\) \(15925248\) \(3.6539\)  
44880.bh3 44880br6 \([0, -1, 0, -201236520, 1098840178800]\) \(220031146443748723000125481/172266701724057600\) \(705604410261739929600\) \([2, 2]\) \(7962624\) \(3.3074\)  
44880.bh4 44880br5 \([0, -1, 0, -39758520, 96434924400]\) \(1696892787277117093383481/1440538624914939000\) \(5900446207651590144000\) \([2]\) \(5308416\) \(3.1046\)  
44880.bh5 44880br4 \([0, -1, 0, -26038200, -50585416848]\) \(476646772170172569823801/5862293314453125000\) \(24011953416000000000000\) \([2]\) \(5308416\) \(3.1046\)  
44880.bh6 44880br3 \([0, -1, 0, -12492840, 17414389872]\) \(-52643812360427830814761/1504091705903677440\) \(-6160759627381462794240\) \([2]\) \(3981312\) \(2.9608\)  
44880.bh7 44880br2 \([0, -1, 0, -3038520, 786668400]\) \(757443433548897303481/373234243041000000\) \(1528767459495936000000\) \([2, 2]\) \(2654208\) \(2.7581\)  
44880.bh8 44880br1 \([0, -1, 0, 693960, 93920112]\) \(9023321954633914439/6156756739584000\) \(-25218075605336064000\) \([2]\) \(1327104\) \(2.4115\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 44880.bh have rank \(1\).

Complex multiplication

The elliptic curves in class 44880.bh do not have complex multiplication.

Modular form 44880.2.a.bh

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + 4 q^{7} + q^{9} - q^{11} + 2 q^{13} - q^{15} - q^{17} + 4 q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 3 & 12 & 4 & 6 & 12 \\ 4 & 1 & 2 & 12 & 3 & 4 & 6 & 12 \\ 2 & 2 & 1 & 6 & 6 & 2 & 3 & 6 \\ 3 & 12 & 6 & 1 & 4 & 12 & 2 & 4 \\ 12 & 3 & 6 & 4 & 1 & 12 & 2 & 4 \\ 4 & 4 & 2 & 12 & 12 & 1 & 6 & 3 \\ 6 & 6 & 3 & 2 & 2 & 6 & 1 & 2 \\ 12 & 12 & 6 & 4 & 4 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.