Properties

Label 14490.h
Number of curves $4$
Conductor $14490$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 14490.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14490.h1 14490k3 \([1, -1, 0, -77280, 8288270]\) \(70016546394529281/1610\) \(1173690\) \([2]\) \(32768\) \(1.1392\)  
14490.h2 14490k2 \([1, -1, 0, -4830, 130400]\) \(17095749786081/2592100\) \(1889640900\) \([2, 2]\) \(16384\) \(0.79263\)  
14490.h3 14490k4 \([1, -1, 0, -4380, 155330]\) \(-12748946194881/6718982410\) \(-4898138176890\) \([2]\) \(32768\) \(1.1392\)  
14490.h4 14490k1 \([1, -1, 0, -330, 1700]\) \(5461074081/1610000\) \(1173690000\) \([2]\) \(8192\) \(0.44605\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 14490.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} + 4 q^{11} - 2 q^{13} + q^{14} + q^{16} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.