Properties

Label 1290.n
Number of curves $4$
Conductor $1290$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1290.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1290.n1 1290n3 \([1, 0, 0, -34306, -1065280]\) \(4465136636671380769/2096375976562500\) \(2096375976562500\) \([2]\) \(8640\) \(1.6342\)  
1290.n2 1290n1 \([1, 0, 0, -17566, 894596]\) \(599437478278595809/33854760000\) \(33854760000\) \([6]\) \(2880\) \(1.0849\) \(\Gamma_0(N)\)-optimal
1290.n3 1290n2 \([1, 0, 0, -16566, 1001196]\) \(-502780379797811809/143268096832200\) \(-143268096832200\) \([6]\) \(5760\) \(1.4315\)  
1290.n4 1290n4 \([1, 0, 0, 121944, -8034030]\) \(200541749524551119231/144008551960031250\) \(-144008551960031250\) \([2]\) \(17280\) \(1.9808\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1290.n have rank \(0\).

Complex multiplication

The elliptic curves in class 1290.n do not have complex multiplication.

Modular form 1290.2.a.n

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + 2q^{7} + q^{8} + q^{9} - q^{10} + q^{12} + 2q^{13} + 2q^{14} - q^{15} + q^{16} - 6q^{17} + q^{18} + 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.