Properties

Label 388080gn
Number of curves $2$
Conductor $388080$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("gn1")
 
E.isogeny_class()
 

Elliptic curves in class 388080gn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388080.gn2 388080gn1 \([0, 0, 0, 1932, 13867]\) \(199344128/136125\) \(-544602366000\) \([2]\) \(368640\) \(0.94058\) \(\Gamma_0(N)\)-optimal
388080.gn1 388080gn2 \([0, 0, 0, -8463, 115738]\) \(1047213232/515625\) \(33006204000000\) \([2]\) \(737280\) \(1.2872\)  

Rank

sage: E.rank()
 

The elliptic curves in class 388080gn have rank \(1\).

Complex multiplication

The elliptic curves in class 388080gn do not have complex multiplication.

Modular form 388080.2.a.gn

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