↑

Properties

Label 7942.k
Number of curves $2$
Conductor $7942$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 7942.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7942.k1 7942c2 \([1, 1, 0, -41743159, -29278902123]\) \(24928563670864867/13279961395712\) \(4285280169376300882523648\) \([2]\) \(1504800\) \(3.4178\)  
7942.k2 7942c1 \([1, 1, 0, -24184119, 45420765845]\) \(4847659921191907/42218553344\) \(13623407782135261822976\) \([2]\) \(752400\) \(3.0712\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7942.k have rank \(1\).

Complex multiplication

The elliptic curves in class 7942.k do not have complex multiplication.

Modular form 7942.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} + q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} - q^{8} + q^{9} - 2 q^{10} - q^{11} + 2 q^{12} - 2 q^{13} - 2 q^{14} + 4 q^{15} + q^{16} - 6 q^{17} - q^{18} + O(q^{20})\) 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.