↑

Properties

Label 163350gf
Number of curves $2$
Conductor $163350$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("gf1")
 
E.isogeny_class()
 

Elliptic curves in class 163350gf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
163350.dn1 163350gf1 \([1, -1, 0, -481542, -128523884]\) \(-16522921323/4000\) \(-2989509187500000\) \([]\) \(1944000\) \(1.9583\) \(\Gamma_0(N)\)-optimal
163350.dn2 163350gf2 \([1, -1, 0, 199083, -453333259]\) \(1601613/163840\) \(-89266266017280000000\) \([]\) \(5832000\) \(2.5076\)  

Rank

sage: E.rank()
 

The elliptic curves in class 163350gf have rank \(1\).

Complex multiplication

The elliptic curves in class 163350gf do not have complex multiplication.

Modular form 163350.2.a.gf

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