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Properties

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

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

Elliptic curves in class 28322.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28322.q1 28322bb2 \([1, 0, 0, -9912995, -11989610879]\) \(37936442980801/88817792\) \(252221288974089959552\) \([2]\) \(3096576\) \(2.7950\)  
28322.q2 28322bb1 \([1, 0, 0, -849955, -35461119]\) \(23912763841/13647872\) \(38756692663485612032\) \([2]\) \(1548288\) \(2.4484\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 28322.q do not have complex multiplication.

Modular form 28322.2.a.q

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

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.