Properties

Label 4290.p
Number of curves $4$
Conductor $4290$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 4290.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4290.p1 4290o4 \([1, 0, 1, -2271573, -1317954464]\) \(1296294060988412126189641/647824320\) \(647824320\) \([2]\) \(41472\) \(1.9269\)  
4290.p2 4290o3 \([1, 0, 1, -141973, -20602144]\) \(-316472948332146183241/7074906009600\) \(-7074906009600\) \([2]\) \(20736\) \(1.5803\)  
4290.p3 4290o2 \([1, 0, 1, -28098, -1802744]\) \(2453170411237305241/19353090685500\) \(19353090685500\) \([6]\) \(13824\) \(1.3776\)  
4290.p4 4290o1 \([1, 0, 1, -598, -64744]\) \(-23592983745241/1794399750000\) \(-1794399750000\) \([6]\) \(6912\) \(1.0310\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4290.p have rank \(0\).

Complex multiplication

The elliptic curves in class 4290.p do not have complex multiplication.

Modular form 4290.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + 2 q^{7} - q^{8} + q^{9} - q^{10} - q^{11} + q^{12} + q^{13} - 2 q^{14} + q^{15} + q^{16} + 6 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.