Properties

Label 1290.h
Number of curves $4$
Conductor $1290$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1290.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1290.h1 1290g4 \([1, 0, 1, -5183, -124342]\) \(15393836938735081/2275690697640\) \(2275690697640\) \([2]\) \(2880\) \(1.0958\)  
1290.h2 1290g3 \([1, 0, 1, -4983, -135782]\) \(13679527032530281/381633600\) \(381633600\) \([2]\) \(1440\) \(0.74920\)  
1290.h3 1290g2 \([1, 0, 1, -1358, 19118]\) \(276670733768281/336980250\) \(336980250\) \([6]\) \(960\) \(0.54647\)  
1290.h4 1290g1 \([1, 0, 1, -108, 118]\) \(137467988281/72562500\) \(72562500\) \([6]\) \(480\) \(0.19989\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1290.h have rank \(0\).

Complex multiplication

The elliptic curves in class 1290.h do not have complex multiplication.

Modular form 1290.2.a.h

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.