↑

Properties

Label 14586b
Number of curves $2$
Conductor $14586$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 14586b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14586.c1 14586b1 \([1, 1, 0, -3020, -59376]\) \(3047678972871625/304559880768\) \(304559880768\) \([2]\) \(21504\) \(0.93988\) \(\Gamma_0(N)\)-optimal
14586.c2 14586b2 \([1, 1, 0, 3740, -279752]\) \(5783051584712375/37533175779528\) \(-37533175779528\) \([2]\) \(43008\) \(1.2865\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14586b have rank \(1\).

Complex multiplication

The elliptic curves in class 14586b do not have complex multiplication.

Modular form 14586.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + 2 q^{7} - q^{8} + q^{9} + q^{11} - q^{12} + q^{13} - 2 q^{14} + q^{16} - q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.