↑

Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("eg1")
 
E.isogeny_class()
 

Elliptic curves in class 73920eg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73920.d1 73920eg1 \([0, -1, 0, -319681, 69673825]\) \(13782741913468081/701662500\) \(183936614400000\) \([2]\) \(552960\) \(1.8071\) \(\Gamma_0(N)\)-optimal
73920.d2 73920eg2 \([0, -1, 0, -302401, 77522401]\) \(-11666347147400401/3126621093750\) \(-819624960000000000\) \([2]\) \(1105920\) \(2.1537\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 73920.2.a.eg

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} - q^{11} - 4 q^{13} + q^{15} - 4 q^{17} + 8 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.