Properties

Label 32490.by
Number of curves $2$
Conductor $32490$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("by1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 32490.by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32490.by1 32490br2 \([1, -1, 1, -11845922, -15689857579]\) \(781484460931/900\) \(211715398512801900\) \([2]\) \(1167360\) \(2.6085\)  
32490.by2 32490br1 \([1, -1, 1, -734342, -249206011]\) \(-186169411/6480\) \(-1524350869292173680\) \([2]\) \(583680\) \(2.2620\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 32490.by have rank \(0\).

Complex multiplication

The elliptic curves in class 32490.by do not have complex multiplication.

Modular form 32490.2.a.by

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + 2 q^{7} + q^{8} + q^{10} + 2 q^{13} + 2 q^{14} + q^{16} + 6 q^{17} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.