Properties

Label 32144v
Number of curves $2$
Conductor $32144$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 32144v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32144.y1 32144v1 \([0, 1, 0, -44, 104]\) \(-768208/41\) \(-514304\) \([]\) \(4608\) \(-0.14519\) \(\Gamma_0(N)\)-optimal
32144.y2 32144v2 \([0, 1, 0, 236, 328]\) \(115393712/68921\) \(-864545024\) \([]\) \(13824\) \(0.40411\)  

Rank

sage: E.rank()
 

The elliptic curves in class 32144v have rank \(0\).

Complex multiplication

The elliptic curves in class 32144v do not have complex multiplication.

Modular form 32144.2.a.v

sage: E.q_eigenform(10)
 
\(q + q^{3} + 3 q^{5} - 2 q^{9} - 3 q^{11} + 4 q^{13} + 3 q^{15} - 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.