↑

Properties

Label 164346.cp
Number of curves $2$
Conductor $164346$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("cp1")
 
E.isogeny_class()
 

Elliptic curves in class 164346.cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
164346.cp1 164346i1 \([1, 0, 0, -333201, -74155131]\) \(-83492334037417941601/127211109998076\) \(-6233344389905724\) \([]\) \(1505280\) \(1.9306\) \(\Gamma_0(N)\)-optimal
164346.cp2 164346i2 \([1, 0, 0, 753409, 4890824217]\) \(965205988173192999359/211441108567651762176\) \(-10360614319814936346624\) \([7]\) \(10536960\) \(2.9036\)  

Rank

sage: E.rank()
 

The elliptic curves in class 164346.cp have rank \(0\).

Complex multiplication

The elliptic curves in class 164346.cp do not have complex multiplication.

Modular form 164346.2.a.cp

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} + q^{9} - q^{10} - 2 q^{11} + q^{12} + q^{13} - q^{15} + q^{16} - 3 q^{17} + q^{18} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.