Properties

Label 18150.g
Number of curves $2$
Conductor $18150$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 18150.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18150.g1 18150c1 \([1, 1, 0, -4167000, -3274506000]\) \(217190179331/97200\) \(3581133055706250000\) \([2]\) \(506880\) \(2.5183\) \(\Gamma_0(N)\)-optimal
18150.g2 18150c2 \([1, 1, 0, -3501500, -4354612500]\) \(-128864147651/147622500\) \(-5438845828353867187500\) \([2]\) \(1013760\) \(2.8649\)  

Rank

sage: E.rank()
 

The elliptic curves in class 18150.g have rank \(1\).

Complex multiplication

The elliptic curves in class 18150.g do not have complex multiplication.

Modular form 18150.2.a.g

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