Properties

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

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("hk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 388080hk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388080.hk2 388080hk1 \([0, 0, 0, -9408, -1101373]\) \(-67108864/343035\) \(-470732501075760\) \([2]\) \(1474560\) \(1.4998\) \(\Gamma_0(N)\)-optimal
388080.hk1 388080hk2 \([0, 0, 0, -227703, -41747902]\) \(59466754384/121275\) \(2662729299014400\) \([2]\) \(2949120\) \(1.8463\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 388080.2.a.hk

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