Properties

Label 288990.ff
Number of curves $4$
Conductor $288990$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("288990.ff1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 288990.ff

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
288990.ff1 288990ff4 [1, -1, 1, -4623872, -3825829159] [2] 7077888  
288990.ff2 288990ff3 [1, -1, 1, -334652, -39561271] [2] 7077888  
288990.ff3 288990ff2 [1, -1, 1, -289022, -59711479] [2, 2] 3538944  
288990.ff4 288990ff1 [1, -1, 1, -15242, -1232071] [2] 1769472 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 288990.ff have rank \(1\).

Modular form 288990.2.a.ff

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{5} - 4q^{7} + q^{8} + q^{10} - 4q^{11} - 4q^{14} + q^{16} + 2q^{17} + q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.