Properties

Label 182.d
Number of curves $3$
Conductor $182$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 182.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
182.d1 182b3 [1, 0, 0, -15663, -755809] [] 108  
182.d2 182b2 [1, 0, 0, -193, -1055] [3] 36  
182.d3 182b1 [1, 0, 0, 7, -7] [3] 12 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 182.2.a.d

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} - 2q^{9} - 3q^{11} + q^{12} + q^{13} + q^{14} + q^{16} - 2q^{18} + 2q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.