Properties

Label 92400dw
Number of curves 4
Conductor 92400
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("92400.z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400dw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
92400.z3 92400dw1 [0, -1, 0, -200408, 30051312] [2] 884736 \(\Gamma_0(N)\)-optimal
92400.z2 92400dw2 [0, -1, 0, -848408, -270620688] [2, 2] 1769472  
92400.z4 92400dw3 [0, -1, 0, 1131592, -1347740688] [2] 3538944  
92400.z1 92400dw4 [0, -1, 0, -13196408, -18446876688] [2] 3538944  

Rank

sage: E.rank()
 

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

Modular form 92400.2.a.z

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.