Properties

Label 10830k
Number of curves $2$
Conductor $10830$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10830k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.i2 10830k1 \([1, 0, 1, -2364, -2438]\) \(212883113611/122880000\) \(842833920000\) \([2]\) \(30720\) \(0.97786\) \(\Gamma_0(N)\)-optimal
10830.i1 10830k2 \([1, 0, 1, -26684, -1675654]\) \(306331959547531/900000000\) \(6173100000000\) \([2]\) \(61440\) \(1.3244\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10830k have rank \(0\).

Complex multiplication

The elliptic curves in class 10830k do not have complex multiplication.

Modular form 10830.2.a.k

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.