Properties

Label 277200hx
Number of curves $4$
Conductor $277200$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("hx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 277200hx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277200.hx3 277200hx1 \([0, 0, 0, -598800, 180991375]\) \(-130287139815424/2250652635\) \(-410181442728750000\) \([2]\) \(3981312\) \(2.1776\) \(\Gamma_0(N)\)-optimal
277200.hx2 277200hx2 \([0, 0, 0, -9620175, 11484774250]\) \(33766427105425744/9823275\) \(28644669900000000\) \([2]\) \(7962624\) \(2.5241\)  
277200.hx4 277200hx3 \([0, 0, 0, 2317200, 867344875]\) \(7549996227362816/6152409907875\) \(-1121276705710218750000\) \([2]\) \(11943936\) \(2.7269\)  
277200.hx1 277200hx4 \([0, 0, 0, -11159175, 7565103250]\) \(52702650535889104/22020583921875\) \(64212022716187500000000\) \([2]\) \(23887872\) \(3.0734\)  

Rank

sage: E.rank()
 

The elliptic curves in class 277200hx have rank \(0\).

Complex multiplication

The elliptic curves in class 277200hx do not have complex multiplication.

Modular form 277200.2.a.hx

sage: E.q_eigenform(10)
 
\(q + q^{7} - q^{11} - 2q^{13} - 6q^{17} - 8q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.