Properties

Label 10830.k
Number of curves $4$
Conductor $10830$
CM no
Rank $1$
Graph

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

Elliptic curves in class 10830.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.k1 10830l3 \([1, 0, 1, -224189, 40779086]\) \(26487576322129/44531250\) \(2095011888281250\) \([2]\) \(92160\) \(1.8351\)  
10830.k2 10830l2 \([1, 0, 1, -18419, 201242]\) \(14688124849/8122500\) \(382130168422500\) \([2, 2]\) \(46080\) \(1.4886\)  
10830.k3 10830l1 \([1, 0, 1, -11199, -454334]\) \(3301293169/22800\) \(1072646086800\) \([2]\) \(23040\) \(1.1420\) \(\Gamma_0(N)\)-optimal
10830.k4 10830l4 \([1, 0, 1, 71831, 1609142]\) \(871257511151/527800050\) \(-24830818344094050\) \([2]\) \(92160\) \(1.8351\)  

Rank

sage: E.rank()
 

The elliptic curves in class 10830.k have rank \(1\).

Complex multiplication

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

Modular form 10830.2.a.k

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.