↑

Properties

Label 38962.h
Number of curves $2$
Conductor $38962$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 38962.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38962.h1 38962h2 \([1, 1, 0, -3811783747, 90580056598673]\) \(3457421777436801623930814481/2690147821103679244\) \(4765760964102255105179884\) \([]\) \(21600000\) \(4.0426\)  
38962.h2 38962h1 \([1, 1, 0, -31300887, -62771540267]\) \(1914421473306136725841/147437307865222144\) \(261194184559020806646784\) \([]\) \(4320000\) \(3.2378\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 38962.h have rank \(1\).

Complex multiplication

The elliptic curves in class 38962.h do not have complex multiplication.

Modular form 38962.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{7} - q^{8} - 2 q^{9} - q^{10} - q^{12} + q^{13} + q^{14} - q^{15} + q^{16} + 2 q^{17} + 2 q^{18} + 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.