Properties

Label 182.c
Number of curves $4$
Conductor $182$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 182.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
182.c1 182a4 [1, -1, 1, -59134, 5547693] [2] 720  
182.c2 182a3 [1, -1, 1, -31294, -2081875] [2] 720  
182.c3 182a2 [1, -1, 1, -4254, 59693] [2, 2] 360  
182.c4 182a1 [1, -1, 1, 866, 6445] [4] 180 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 182.c have rank \(0\).

Complex multiplication

The elliptic curves in class 182.c do not have complex multiplication.

Modular form 182.2.a.c

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + 2q^{5} - q^{7} + q^{8} - 3q^{9} + 2q^{10} + 4q^{11} - q^{13} - q^{14} + q^{16} - 6q^{17} - 3q^{18} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.