Properties

Label 480240do
Number of curves $2$
Conductor $480240$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("do1")
 
E.isogeny_class()
 

Elliptic curves in class 480240do

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
480240.do1 480240do1 \([0, 0, 0, -53787, 4801034]\) \(5763259856089/450225\) \(1344364646400\) \([2]\) \(884736\) \(1.3745\) \(\Gamma_0(N)\)-optimal
480240.do2 480240do2 \([0, 0, 0, -50187, 5471354]\) \(-4681768588489/1621620405\) \(-4842132583403520\) \([2]\) \(1769472\) \(1.7211\)  

Rank

sage: E.rank()
 

The elliptic curves in class 480240do have rank \(0\).

Complex multiplication

The elliptic curves in class 480240do do not have complex multiplication.

Modular form 480240.2.a.do

sage: E.q_eigenform(10)
 
\(q + q^{5} + 2 q^{11} + 2 q^{13} + 4 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.