Properties

Label 28224.eo
Number of curves $2$
Conductor $28224$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("eo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28224.eo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.eo1 28224o1 \([0, 0, 0, -10584, 370440]\) \(55296/7\) \(16598831993856\) \([2]\) \(73728\) \(1.2659\) \(\Gamma_0(N)\)-optimal
28224.eo2 28224o2 \([0, 0, 0, 15876, 1926288]\) \(11664/49\) \(-1859069183311872\) \([2]\) \(147456\) \(1.6125\)  

Rank

sage: E.rank()
 

The elliptic curves in class 28224.eo have rank \(0\).

Complex multiplication

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

Modular form 28224.2.a.eo

sage: E.q_eigenform(10)
 
\(q + 2q^{5} - 6q^{11} - 6q^{13} + 2q^{17} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.