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Properties

Label 28322.s
Number of curves $2$
Conductor $28322$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 28322.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28322.s1 28322bi1 \([1, 1, 1, -99422, -12110253]\) \(-11060825617/2744\) \(-26962988881976\) \([]\) \(145152\) \(1.5647\) \(\Gamma_0(N)\)-optimal
28322.s2 28322bi2 \([1, 1, 1, 42188, -42698013]\) \(845095823/80707214\) \(-793042169743898606\) \([]\) \(435456\) \(2.1140\)  

Rank

sage: E.rank()
 

The elliptic curves in class 28322.s have rank \(0\).

Complex multiplication

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

Modular form 28322.2.a.s

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.