↑

Properties

Label 43890i
Number of curves $2$
Conductor $43890$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 43890i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43890.j2 43890i1 \([1, 1, 0, 173, -359]\) \(567457901639/408615900\) \(-408615900\) \([2]\) \(21504\) \(0.34074\) \(\Gamma_0(N)\)-optimal
43890.j1 43890i2 \([1, 1, 0, -777, -3969]\) \(51982817627161/24342754590\) \(24342754590\) \([2]\) \(43008\) \(0.68731\)  

Rank

sage: E.rank()
 

The elliptic curves in class 43890i have rank \(0\).

Complex multiplication

The elliptic curves in class 43890i do not have complex multiplication.

Modular form 43890.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{7} - q^{8} + q^{9} - q^{10} - q^{11} - q^{12} + 2 q^{13} + q^{14} - q^{15} + q^{16} - q^{18} - q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.