Properties

Label 22080.n
Number of curves $2$
Conductor $22080$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 22080.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22080.n1 22080c2 \([0, -1, 0, -2074881, 1151060481]\) \(7536914291382802562/17961229575\) \(2354214282854400\) \([2]\) \(337920\) \(2.1910\)  
22080.n2 22080c1 \([0, -1, 0, -128161, 18458785]\) \(-3552342505518244/179863605135\) \(-11787541226127360\) \([2]\) \(168960\) \(1.8444\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 22080.n have rank \(1\).

Complex multiplication

The elliptic curves in class 22080.n do not have complex multiplication.

Modular form 22080.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} - 2 q^{11} + q^{15} + 6 q^{17} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.