Properties

Label 119952gs
Number of curves $6$
Conductor $119952$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("gs1")
 
E.isogeny_class()
 

Elliptic curves in class 119952gs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.bx5 119952gs1 \([0, 0, 0, -495641811, -4241860146286]\) \(38331145780597164097/55468445663232\) \(19485955778292453224742912\) \([2]\) \(35389440\) \(3.7548\) \(\Gamma_0(N)\)-optimal
119952.bx4 119952gs2 \([0, 0, 0, -640148691, -1566719882350]\) \(82582985847542515777/44772582831427584\) \(15728520219044826202446495744\) \([2, 2]\) \(70778880\) \(4.1014\)  
119952.bx6 119952gs3 \([0, 0, 0, 2469007149, -12322533595246]\) \(4738217997934888496063/2928751705237796928\) \(-1028864709142041498010731675648\) \([2]\) \(141557760\) \(4.4480\)  
119952.bx2 119952gs4 \([0, 0, 0, -6061414611, 180398070722450]\) \(70108386184777836280897/552468975892674624\) \(194081263760003951884752912384\) \([2, 2]\) \(141557760\) \(4.4480\)  
119952.bx3 119952gs5 \([0, 0, 0, -2064613971, 414744081367826]\) \(-2770540998624539614657/209924951154647363208\) \(-73746222127712565105575019184128\) \([2]\) \(283115520\) \(4.7945\)  
119952.bx1 119952gs6 \([0, 0, 0, -96798469971, 11591798658784274]\) \(285531136548675601769470657/17941034271597192\) \(6302650024767289886032822272\) \([2]\) \(283115520\) \(4.7945\)  

Rank

sage: E.rank()
 

The elliptic curves in class 119952gs have rank \(1\).

Complex multiplication

The elliptic curves in class 119952gs do not have complex multiplication.

Modular form 119952.2.a.gs

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.