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Properties

Label 166635.q
Number of curves $2$
Conductor $166635$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 166635.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
166635.q1 166635q1 \([1, -1, 1, -19754282, -32934422744]\) \(292583028222603/8456021875\) \(24639075388514341715625\) \([2]\) \(13685760\) \(3.0745\) \(\Gamma_0(N)\)-optimal
166635.q2 166635q2 \([1, -1, 1, 4741063, -109252119626]\) \(4044759171237/1771943359375\) \(-5163071555537808486328125\) \([2]\) \(27371520\) \(3.4211\)  

Rank

sage: E.rank()
 

The elliptic curves in class 166635.q have rank \(0\).

Complex multiplication

The elliptic curves in class 166635.q do not have complex multiplication.

Modular form 166635.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + q^{5} + q^{7} + 3 q^{8} - q^{10} + 4 q^{11} + 4 q^{13} - q^{14} - q^{16} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.