Properties

Label 92400.hs
Number of curves $4$
Conductor $92400$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("hs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400.hs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.hs1 92400hh4 \([0, 1, 0, -1239908, -280602312]\) \(52702650535889104/22020583921875\) \(88082335687500000000\) \([2]\) \(2985984\) \(2.5241\)  
92400.hs2 92400hh2 \([0, 1, 0, -1068908, -425718312]\) \(33766427105425744/9823275\) \(39293100000000\) \([2]\) \(995328\) \(1.9748\)  
92400.hs3 92400hh1 \([0, 1, 0, -66533, -6725562]\) \(-130287139815424/2250652635\) \(-562663158750000\) \([2]\) \(497664\) \(1.6283\) \(\Gamma_0(N)\)-optimal
92400.hs4 92400hh3 \([0, 1, 0, 257467, -32038062]\) \(7549996227362816/6152409907875\) \(-1538102476968750000\) \([2]\) \(1492992\) \(2.1776\)  

Rank

sage: E.rank()
 

The elliptic curves in class 92400.hs have rank \(1\).

Complex multiplication

The elliptic curves in class 92400.hs do not have complex multiplication.

Modular form 92400.2.a.hs

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} + q^{11} - 2q^{13} + 6q^{17} - 8q^{19} + O(q^{20})\)  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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.