Properties

Label 28224.v
Number of curves $2$
Conductor $28224$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 28224.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.v1 28224f2 \([0, 0, 0, -2630124, -1641938256]\) \(-67645179/8\) \(-237960855463919616\) \([]\) \(580608\) \(2.3598\)  
28224.v2 28224f1 \([0, 0, 0, 4116, -6953296]\) \(189/512\) \(-20890939299987456\) \([]\) \(193536\) \(1.8105\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 28224.v have rank \(1\).

Complex multiplication

The elliptic curves in class 28224.v do not have complex multiplication.

Modular form 28224.2.a.v

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