Properties

Label 288990ej
Number of curves $4$
Conductor $288990$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("288990.ej1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 288990ej

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
288990.ej3 288990ej1 [1, -1, 1, -47183, -3909369] [2] 1179648 \(\Gamma_0(N)\)-optimal
288990.ej2 288990ej2 [1, -1, 1, -77603, 1773087] [2, 2] 2359296  
288990.ej1 288990ej3 [1, -1, 1, -944573, 353069331] [2] 4718592  
288990.ej4 288990ej4 [1, -1, 1, 302647, 13788987] [2] 4718592  

Rank

sage: E.rank()
 

The elliptic curves in class 288990ej have rank \(0\).

Modular form 288990.2.a.ej

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} + 4q^{11} + q^{16} - 2q^{17} + q^{19} + O(q^{20}) \)

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.