Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("28322.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28322.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28322.q1 28322bb2 [1, 0, 0, -9912995, -11989610879] [2] 3096576  
28322.q2 28322bb1 [1, 0, 0, -849955, -35461119] [2] 1548288 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 28322.2.a.q

sage: E.q_eigenform(10)
 
\( q + q^{2} - 2q^{3} + q^{4} - 4q^{5} - 2q^{6} + q^{8} + q^{9} - 4q^{10} + 6q^{11} - 2q^{12} + 2q^{13} + 8q^{15} + q^{16} + q^{18} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.