Properties

Label 106560.n
Number of curves $2$
Conductor $106560$
CM no
Rank $0$
Graph

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

Elliptic curves in class 106560.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
106560.n1 106560fh1 \([0, 0, 0, -276528, -55967848]\) \(3132662187311104/151723125\) \(113260705920000\) \([2]\) \(688128\) \(1.7694\) \(\Gamma_0(N)\)-optimal
106560.n2 106560fh2 \([0, 0, 0, -261948, -62132272]\) \(-166426126492624/43316015625\) \(-517363718400000000\) \([2]\) \(1376256\) \(2.1160\)  

Rank

sage: E.rank()
 

The elliptic curves in class 106560.n have rank \(0\).

Complex multiplication

The elliptic curves in class 106560.n do not have complex multiplication.

Modular form 106560.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{5} - 4 q^{7} + 4 q^{11} - 2 q^{13} - 2 q^{17} - 2 q^{19} + O(q^{20})\) 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.