Properties

Label 59290cd
Number of curves $4$
Conductor $59290$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cd1")
 
E.isogeny_class()
 

Elliptic curves in class 59290cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
59290.by3 59290cd1 \([1, 1, 0, -332147, 1433680109]\) \(-19443408769/4249907200\) \(-885775773781377740800\) \([2]\) \(3317760\) \(2.6987\) \(\Gamma_0(N)\)-optimal
59290.by2 59290cd2 \([1, 1, 0, -21202227, 37234215341]\) \(5057359576472449/51765560000\) \(10789101221839934840000\) \([2]\) \(6635520\) \(3.0453\)  
59290.by4 59290cd3 \([1, 1, 0, 2988093, -38622359299]\) \(14156681599871/3100231750000\) \(-646157680162485625750000\) \([2]\) \(9953280\) \(3.2480\)  
59290.by1 59290cd4 \([1, 1, 0, -154841887, -720668834871]\) \(1969902499564819009/63690429687500\) \(13274510944359854492187500\) \([2]\) \(19906560\) \(3.5946\)  

Rank

sage: E.rank()
 

The elliptic curves in class 59290cd have rank \(0\).

Complex multiplication

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

Modular form 59290.2.a.cd

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