Properties

Label 22080.cv
Number of curves $2$
Conductor $22080$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cv1")
 
E.isogeny_class()
 

Elliptic curves in class 22080.cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22080.cv1 22080cv2 \([0, 1, 0, -50305, 2990975]\) \(53706380371489/16171875000\) \(4239360000000000\) \([2]\) \(92160\) \(1.7038\)  
22080.cv2 22080cv1 \([0, 1, 0, 8575, 317823]\) \(265971760991/317400000\) \(-83204505600000\) \([2]\) \(46080\) \(1.3573\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 22080.cv have rank \(0\).

Complex multiplication

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

Modular form 22080.2.a.cv

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{9} + 2 q^{11} + q^{15} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.