Properties

Label 182070.cp
Number of curves $4$
Conductor $182070$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 182070.cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
182070.cp1 182070bb4 [1, -1, 1, -971528, -368336059] [2] 2359296  
182070.cp2 182070bb2 [1, -1, 1, -61178, -5652619] [2, 2] 1179648  
182070.cp3 182070bb1 [1, -1, 1, -9158, 215237] [2] 589824 \(\Gamma_0(N)\)-optimal
182070.cp4 182070bb3 [1, -1, 1, 16852, -19136203] [2] 2359296  

Rank

sage: E.rank()
 

The elliptic curves in class 182070.cp have rank \(0\).

Complex multiplication

The elliptic curves in class 182070.cp do not have complex multiplication.

Modular form 182070.2.a.cp

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} - q^{5} + q^{7} + q^{8} - q^{10} - 4q^{11} - 2q^{13} + q^{14} + q^{16} + O(q^{20}) \)

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 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.