Properties

Label 92400.cw
Number of curves $6$
Conductor $92400$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400.cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.cw1 92400be6 \([0, -1, 0, -12806640008, 557833047898512]\) \(7259042500647479362626220802/12006225\) \(384199200000000\) \([2]\) \(56623104\) \(3.9331\)  
92400.cw2 92400be4 \([0, -1, 0, -800415008, 8716341298512]\) \(3544454449806874081077604/144149438750625\) \(2306391020010000000000\) \([2, 2]\) \(28311552\) \(3.5865\)  
92400.cw3 92400be5 \([0, -1, 0, -799190008, 8744349698512]\) \(-1764102724103262766456802/11303622506742021225\) \(-361715920215744679200000000\) \([2]\) \(56623104\) \(3.9331\)  
92400.cw4 92400be3 \([0, -1, 0, -81040008, -51837451488]\) \(3678765970528905177604/2056287578994061875\) \(32900601263904990000000000\) \([2]\) \(28311552\) \(3.5865\)  
92400.cw5 92400be2 \([0, -1, 0, -50102508, 135767548512]\) \(3477299736386222510416/22070630703515625\) \(88282522814062500000000\) \([2, 2]\) \(14155776\) \(3.2400\)  
92400.cw6 92400be1 \([0, -1, 0, -1274383, 4615204762]\) \(-915553975060166656/36269989013671875\) \(-9067497253417968750000\) \([2]\) \(7077888\) \(2.8934\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 92400.2.a.cw

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.