Properties

Label 162240hb
Number of curves $4$
Conductor $162240$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("hb1")
 
E.isogeny_class()
 

Elliptic curves in class 162240hb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162240.de4 162240hb1 \([0, -1, 0, 620, 15742]\) \(85184/405\) \(-125110889280\) \([2]\) \(147456\) \(0.81170\) \(\Gamma_0(N)\)-optimal
162240.de3 162240hb2 \([0, -1, 0, -6985, 202825]\) \(1906624/225\) \(4448387174400\) \([2, 2]\) \(294912\) \(1.1583\)  
162240.de1 162240hb3 \([0, -1, 0, -108385, 13770145]\) \(890277128/15\) \(2372473159680\) \([2]\) \(589824\) \(1.5049\)  
162240.de2 162240hb4 \([0, -1, 0, -27265, -1512863]\) \(14172488/1875\) \(296559144960000\) \([2]\) \(589824\) \(1.5049\)  

Rank

sage: E.rank()
 

The elliptic curves in class 162240hb have rank \(0\).

Complex multiplication

The elliptic curves in class 162240hb do not have complex multiplication.

Modular form 162240.2.a.hb

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} - q^{15} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.