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Properties

Label 22743k
Number of curves $2$
Conductor $22743$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 22743k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22743.p2 22743k1 \([1, -1, 0, -495, -1512]\) \(2685619/1323\) \(6615279153\) \([2]\) \(19200\) \(0.57755\) \(\Gamma_0(N)\)-optimal
22743.p1 22743k2 \([1, -1, 0, -6480, -199017]\) \(6018636259/5103\) \(25516076733\) \([2]\) \(38400\) \(0.92413\)  

Rank

sage: E.rank()
 

The elliptic curves in class 22743k have rank \(0\).

Complex multiplication

The elliptic curves in class 22743k do not have complex multiplication.

Modular form 22743.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + 4 q^{5} - q^{7} - 3 q^{8} + 4 q^{10} + 4 q^{11} - 2 q^{13} - q^{14} - q^{16} + O(q^{20})\) 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 Cremona 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 Cremona labels.