Properties

Label 162.c
Number of curves $4$
Conductor $162$
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 162.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162.c1 162b4 \([1, -1, 1, -9695, -364985]\) \(-189613868625/128\) \(-68024448\) \([]\) \(126\) \(0.81867\)  
162.c2 162b3 \([1, -1, 1, -95, -697]\) \(-1159088625/2097152\) \(-169869312\) \([3]\) \(42\) \(0.26937\)  
162.c3 162b1 \([1, -1, 1, -5, 5]\) \(-140625/8\) \(-648\) \([3]\) \(6\) \(-0.70359\) \(\Gamma_0(N)\)-optimal
162.c4 162b2 \([1, -1, 1, 25, 1]\) \(3375/2\) \(-1062882\) \([]\) \(18\) \(-0.15428\)  

Rank

sage: E.rank()
 

The elliptic curves in class 162.c have rank \(0\).

Complex multiplication

The elliptic curves in class 162.c do not have complex multiplication.

Modular form 162.2.a.c

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 2q^{7} + q^{8} - 3q^{11} + 2q^{13} + 2q^{14} + q^{16} - 3q^{17} - q^{19} + O(q^{20})\)  Toggle raw display

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 21 & 7 \\ 3 & 1 & 7 & 21 \\ 21 & 7 & 1 & 3 \\ 7 & 21 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.