Properties

Label 73920gp
Number of curves $2$
Conductor $73920$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("gp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 73920gp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
73920.ff2 73920gp1 [0, 1, 0, -35761, -3060211] [] 480000 \(\Gamma_0(N)\)-optimal
73920.ff1 73920gp2 [0, 1, 0, -107161, 255232229] [] 2400000  

Rank

sage: E.rank()
 

The elliptic curves in class 73920gp have rank \(0\).

Complex multiplication

The elliptic curves in class 73920gp do not have complex multiplication.

Modular form 73920.2.a.gp

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{5} - q^{7} + q^{9} + q^{11} + 6q^{13} - q^{15} - 7q^{17} - 5q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.