Properties

Label 162.d
Number of curves $2$
Conductor $162$
CM no
Rank $0$
Graph

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

Elliptic curves in class 162.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162.d1 162d2 \([1, -1, 1, -56, -161]\) \(-35937/4\) \(-2125764\) \([]\) \(36\) \(-0.048500\)  
162.d2 162d1 \([1, -1, 1, 4, -1]\) \(109503/64\) \(-5184\) \([3]\) \(12\) \(-0.59781\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 162.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 3 q^{5} - 4 q^{7} + q^{8} + 3 q^{10} - q^{13} - 4 q^{14} + q^{16} + 3 q^{17} - 4 q^{19} + O(q^{20})\) Copy content 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.