Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("gq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400.gq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.gq1 92400cl4 \([0, 1, 0, -251533408, -1535554874812]\) \(109999511474021786850916/38201625\) \(611226000000000\) \([2]\) \(8847360\) \(3.0985\)  
92400.gq2 92400cl2 \([0, 1, 0, -15720908, -23996749812]\) \(107422839278466723664/2001871265625\) \(8007485062500000000\) \([2, 2]\) \(4423680\) \(2.7519\)  
92400.gq3 92400cl3 \([0, 1, 0, -15206408, -25640062812]\) \(-24304331176056594436/3678122314453125\) \(-58849957031250000000000\) \([2]\) \(8847360\) \(3.0985\)  
92400.gq4 92400cl1 \([0, 1, 0, -1014783, -349300812]\) \(462278484549842944/57095309704125\) \(14273827426031250000\) \([2]\) \(2211840\) \(2.4054\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 92400.2.a.gq

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} - q^{11} - 6 q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.