Properties

Label 41280cj
Number of curves $2$
Conductor $41280$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("cj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 41280cj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
41280.bs2 41280cj1 [0, -1, 0, -656385, 212472225] [2] 967680 \(\Gamma_0(N)\)-optimal
41280.bs1 41280cj2 [0, -1, 0, -10609665, 13305016737] [2] 1935360  

Rank

sage: E.rank()
 

The elliptic curves in class 41280cj have rank \(1\).

Complex multiplication

The elliptic curves in class 41280cj do not have complex multiplication.

Modular form 41280.2.a.cj

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{5} + 4q^{7} + q^{9} - 4q^{11} - 4q^{13} - q^{15} + 4q^{17} + 4q^{19} + O(q^{20}) \)

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.