Properties

Label 228888u
Number of curves 4
Conductor 228888
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("228888.bz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 228888u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
228888.bz3 228888u1 [0, 0, 0, -32079, 2132242] [2] 589824 \(\Gamma_0(N)\)-optimal
228888.bz2 228888u2 [0, 0, 0, -84099, -6534290] [2, 2] 1179648  
228888.bz4 228888u3 [0, 0, 0, 228021, -43676570] [2] 2359296  
228888.bz1 228888u4 [0, 0, 0, -1228539, -524050058] [2] 2359296  

Rank

sage: E.rank()
 

The elliptic curves in class 228888u have rank \(0\).

Modular form 228888.2.a.bz

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.