Properties

Label 85176ce
Number of curves $4$
Conductor $85176$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ce1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 85176ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
85176.bs4 85176ce1 [0, 0, 0, 1521, -118638] [2] 147456 \(\Gamma_0(N)\)-optimal
85176.bs3 85176ce2 [0, 0, 0, -28899, -1779570] [2, 2] 294912  
85176.bs2 85176ce3 [0, 0, 0, -89739, 8186022] [2] 589824  
85176.bs1 85176ce4 [0, 0, 0, -454779, -118044810] [2] 589824  

Rank

sage: E.rank()
 

The elliptic curves in class 85176ce have rank \(0\).

Complex multiplication

The elliptic curves in class 85176ce do not have complex multiplication.

Modular form 85176.2.a.ce

sage: E.q_eigenform(10)
 
\( q + 2q^{5} + q^{7} - 4q^{11} + 6q^{17} - 8q^{19} + O(q^{20}) \)

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.