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Properties

Label 4290l
Number of curves $2$
Conductor $4290$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 4290l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4290.j2 4290l1 \([1, 0, 1, -4074, -392378]\) \(-7475384530020889/62069784455250\) \(-62069784455250\) \([3]\) \(15120\) \(1.3293\) \(\Gamma_0(N)\)-optimal
4290.j1 4290l2 \([1, 0, 1, -552039, -157917614]\) \(-18605093748570727251049/91759078125000\) \(-91759078125000\) \([]\) \(45360\) \(1.8786\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4290.2.a.l

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.