Properties

Label 176400dx
Number of curves $4$
Conductor $176400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("dx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 176400dx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176400.cj3 176400dx1 [0, 0, 0, -621075, 118935250] [2] 3538944 \(\Gamma_0(N)\)-optimal
176400.cj2 176400dx2 [0, 0, 0, -4149075, -3165632750] [2, 2] 7077888  
176400.cj4 176400dx3 [0, 0, 0, 1142925, -10685564750] [2] 14155776  
176400.cj1 176400dx4 [0, 0, 0, -65889075, -205858052750] [2] 14155776  

Rank

sage: E.rank()
 

The elliptic curves in class 176400dx have rank \(0\).

Complex multiplication

The elliptic curves in class 176400dx do not have complex multiplication.

Modular form 176400.2.a.dx

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

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.