↑

Properties

Label 14490.bn
Number of curves $2$
Conductor $14490$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bn1")
 
E.isogeny_class()
 

Elliptic curves in class 14490.bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14490.bn1 14490br2 \([1, -1, 1, -6638, 2031]\) \(44365623586201/25674468750\) \(18716687718750\) \([2]\) \(36864\) \(1.2362\)  
14490.bn2 14490br1 \([1, -1, 1, -4568, 119607]\) \(14457238157881/49990500\) \(36443074500\) \([2]\) \(18432\) \(0.88960\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 14490.bn have rank \(1\).

Complex multiplication

The elliptic curves in class 14490.bn do not have complex multiplication.

Modular form 14490.2.a.bn

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