Properties

Label 229320cp
Number of curves $2$
Conductor $229320$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 229320cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.y1 229320cp1 \([0, 0, 0, -510678, -140239323]\) \(397526095872/739375\) \(27394556708610000\) \([2]\) \(2064384\) \(2.0448\) \(\Gamma_0(N)\)-optimal
229320.y2 229320cp2 \([0, 0, 0, -345303, -232617798]\) \(-7680778992/34987225\) \(-20740966775222803200\) \([2]\) \(4128768\) \(2.3913\)  

Rank

sage: E.rank()
 

The elliptic curves in class 229320cp have rank \(1\).

Complex multiplication

The elliptic curves in class 229320cp do not have complex multiplication.

Modular form 229320.2.a.cp

sage: E.q_eigenform(10)
 
\(q - q^{5} - 2q^{11} - q^{13} - 6q^{17} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.