Properties

Label 59290.bc
Number of curves $4$
Conductor $59290$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("bc1")
 
E.isogeny_class()
 

Elliptic curves in class 59290.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
59290.bc1 59290br4 \([1, -1, 0, -1587119, -769160925]\) \(2121328796049/120050\) \(25021106729684450\) \([2]\) \(983040\) \(2.2109\)  
59290.bc2 59290br3 \([1, -1, 0, -519899, 134964143]\) \(74565301329/5468750\) \(1139809891111718750\) \([2]\) \(983040\) \(2.2109\)  
59290.bc3 59290br2 \([1, -1, 0, -104869, -10545375]\) \(611960049/122500\) \(25531741560902500\) \([2, 2]\) \(491520\) \(1.8643\)  
59290.bc4 59290br1 \([1, -1, 0, 13711, -987827]\) \(1367631/2800\) \(-583582664249200\) \([2]\) \(245760\) \(1.5177\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 59290.bc have rank \(2\).

Complex multiplication

The elliptic curves in class 59290.bc do not have complex multiplication.

Modular form 59290.2.a.bc

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