Properties

Label 288.b
Number of curves 4
Conductor 288
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("288.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 288.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
288.b1 288b2 [0, 0, 0, -291, -1910] [2] 64  
288.b2 288b3 [0, 0, 0, -156, 736] [4] 64  
288.b3 288b1 [0, 0, 0, -21, -20] [2, 2] 32 \(\Gamma_0(N)\)-optimal
288.b4 288b4 [0, 0, 0, 69, -146] [2] 64  

Rank

sage: E.rank()
 

The elliptic curves in class 288.b have rank \(1\).

Modular form 288.2.a.b

sage: E.q_eigenform(10)
 
\( q - 2q^{5} - 4q^{7} - 4q^{11} - 2q^{13} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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.