↑

Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 7942.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7942.q1 7942p2 \([1, -1, 1, -301398607, -2013927005417]\) \(178286568215258258721/180224\) \(3060845665501184\) \([]\) \(670320\) \(3.1590\)  
7942.q2 7942p1 \([1, -1, 1, -357097, 60765917]\) \(296518892481/77948684\) \(1323846388676988044\) \([]\) \(95760\) \(2.1860\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7942.2.a.q

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.