Properties

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

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 22080t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22080.bb2 22080t1 \([0, -1, 0, 8575, -317823]\) \(265971760991/317400000\) \(-83204505600000\) \([2]\) \(46080\) \(1.3573\) \(\Gamma_0(N)\)-optimal
22080.bb1 22080t2 \([0, -1, 0, -50305, -2990975]\) \(53706380371489/16171875000\) \(4239360000000000\) \([2]\) \(92160\) \(1.7038\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 22080.2.a.t

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 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.