↑

Properties

Label 364650.cx
Number of curves $2$
Conductor $364650$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("cx1")
 
E.isogeny_class()
 

Elliptic curves in class 364650.cx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
364650.cx1 364650cx1 \([1, 0, 1, -2108451, -1178503202]\) \(66342819962001390625/4812668669952\) \(75197947968000000\) \([2]\) \(8515584\) \(2.2894\) \(\Gamma_0(N)\)-optimal
364650.cx2 364650cx2 \([1, 0, 1, -1972451, -1337079202]\) \(-54315282059491182625/17983956399469632\) \(-280999318741713000000\) \([2]\) \(17031168\) \(2.6360\)  

Rank

sage: E.rank()
 

The elliptic curves in class 364650.cx have rank \(1\).

Complex multiplication

The elliptic curves in class 364650.cx do not have complex multiplication.

Modular form 364650.2.a.cx

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} + 4 q^{7} - q^{8} + q^{9} + q^{11} + q^{12} + q^{13} - 4 q^{14} + q^{16} + q^{17} - q^{18} + 2 q^{19} + O(q^{20})\) 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.