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Properties

Label 169650.q
Number of curves $2$
Conductor $169650$
CM no
Rank $1$
Graph

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

Elliptic curves in class 169650.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169650.q1 169650fd1 \([1, -1, 0, -1683915567, 26844957863341]\) \(-1251701744499641551742491347/13559824919198275993600\) \(-5720551137786772684800000000\) \([]\) \(113218560\) \(4.1420\) \(\Gamma_0(N)\)-optimal
169650.q2 169650fd2 \([1, -1, 0, 5592548433, 139523041719341]\) \(62898697943298124177490037/63744399417968386000000\) \(-19604390839747995963093750000000\) \([]\) \(339655680\) \(4.6913\)  

Rank

sage: E.rank()
 

The elliptic curves in class 169650.q have rank \(1\).

Complex multiplication

The elliptic curves in class 169650.q do not have complex multiplication.

Modular form 169650.2.a.q

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