Properties

Label 73920.go
Number of curves $4$
Conductor $73920$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("go1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 73920.go

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73920.go1 73920hh4 \([0, 1, 0, -198385, -17998225]\) \(52702650535889104/22020583921875\) \(360785246976000000\) \([2]\) \(995328\) \(2.0660\)  
73920.go2 73920hh2 \([0, 1, 0, -171025, -27280177]\) \(33766427105425744/9823275\) \(160944537600\) \([2]\) \(331776\) \(1.5167\)  
73920.go3 73920hh1 \([0, 1, 0, -10645, -432565]\) \(-130287139815424/2250652635\) \(-2304668298240\) \([2]\) \(165888\) \(1.1701\) \(\Gamma_0(N)\)-optimal
73920.go4 73920hh3 \([0, 1, 0, 41195, -2042197]\) \(7549996227362816/6152409907875\) \(-6300067745664000\) \([2]\) \(497664\) \(1.7194\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 73920.2.a.go

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - q^{7} + q^{9} - q^{11} - 2q^{13} + q^{15} - 6q^{17} + 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.