Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("bk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28224bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.dr1 28224bk1 \([0, 0, 0, -3675, -80948]\) \(1000000/63\) \(345808999872\) \([2]\) \(24576\) \(0.96514\) \(\Gamma_0(N)\)-optimal
28224.dr2 28224bk2 \([0, 0, 0, 2940, -340256]\) \(8000/147\) \(-51640810647552\) \([2]\) \(49152\) \(1.3117\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 28224.2.a.bk

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