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Properties

Label 22743l
Number of curves $2$
Conductor $22743$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 22743l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22743.i2 22743l1 \([1, -1, 1, -178763, 11264514]\) \(2685619/1323\) \(311221635813818793\) \([2]\) \(364800\) \(2.0498\) \(\Gamma_0(N)\)-optimal
22743.i1 22743l2 \([1, -1, 1, -2339348, 1376754234]\) \(6018636259/5103\) \(1200426309567586773\) \([2]\) \(729600\) \(2.3963\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 22743.2.a.l

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.