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Properties

Label 4290.c
Number of curves $4$
Conductor $4290$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 4290.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4290.c1 4290d3 \([1, 1, 0, -1877518, -990978668]\) \(731941550287276688155369/6103466141778720\) \(6103466141778720\) \([2]\) \(61440\) \(2.1986\)  
4290.c2 4290d4 \([1, 1, 0, -410318, 84102612]\) \(7639889435562537422569/1353152783913696480\) \(1353152783913696480\) \([2]\) \(61440\) \(2.1986\)  
4290.c3 4290d2 \([1, 1, 0, -119918, -14807628]\) \(190713967472892532969/16282209155097600\) \(16282209155097600\) \([2, 2]\) \(30720\) \(1.8520\)  
4290.c4 4290d1 \([1, 1, 0, 8082, -1060428]\) \(58370885971339031/522656808960000\) \(-522656808960000\) \([2]\) \(15360\) \(1.5054\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4290.c have rank \(1\).

Complex multiplication

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

Modular form 4290.2.a.c

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.