Properties

Label 73920.gh
Number of curves $6$
Conductor $73920$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("gh1")
 
E.isogeny_class()
 

Elliptic curves in class 73920.gh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73920.gh1 73920cv4 \([0, 1, 0, -5709499521, 166050503697375]\) \(78519570041710065450485106721/96428056919040\) \(25278036552984821760\) \([2]\) \(35389440\) \(3.8972\)  
73920.gh2 73920cv6 \([0, 1, 0, -1679271041, -24243507729441]\) \(1997773216431678333214187041/187585177195046990066400\) \(49174328690618398163966361600\) \([2]\) \(70778880\) \(4.2437\)  
73920.gh3 73920cv3 \([0, 1, 0, -372903041, 2348135457759]\) \(21876183941534093095979041/3572502915711058560000\) \(936510204336159735152640000\) \([2, 2]\) \(35389440\) \(3.8972\)  
73920.gh4 73920cv2 \([0, 1, 0, -356846721, 2594404082655]\) \(19170300594578891358373921/671785075055001600\) \(176104426715218339430400\) \([2, 2]\) \(17694720\) \(3.5506\)  
73920.gh5 73920cv1 \([0, 1, 0, -21302401, 44334359519]\) \(-4078208988807294650401/880065599546327040\) \(-230703916527472355573760\) \([2]\) \(8847360\) \(3.2040\) \(\Gamma_0(N)\)-optimal
73920.gh6 73920cv5 \([0, 1, 0, 676563839, 13178843552735]\) \(130650216943167617311657439/361816948816603087500000\) \(-94848142230579599769600000000\) \([2]\) \(70778880\) \(4.2437\)  

Rank

sage: E.rank()
 

The elliptic curves in class 73920.gh have rank \(0\).

Complex multiplication

The elliptic curves in class 73920.gh do not have complex multiplication.

Modular form 73920.2.a.gh

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.