Properties

Label 28322.j
Number of curves 2
Conductor 28322
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("28322.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28322.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28322.j1 28322b1 [1, 1, 0, -64019, 7031879] [] 241920 \(\Gamma_0(N)\)-optimal
28322.j2 28322b2 [1, 1, 0, 431616, -27166936] [] 725760  

Rank

sage: E.rank()
 

The elliptic curves in class 28322.j have rank \(1\).

Modular form 28322.2.a.j

sage: E.q_eigenform(10)
 
\( q - q^{2} + 2q^{3} + q^{4} - 3q^{5} - 2q^{6} - q^{8} + q^{9} + 3q^{10} + 2q^{12} + 2q^{13} - 6q^{15} + q^{16} - q^{18} - 7q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.