Properties

Label 10830.p
Number of curves $4$
Conductor $10830$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10830.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.p1 10830p3 \([1, 0, 1, -177785288, -912428607022]\) \(13209596798923694545921/92340\) \(4344216651540\) \([2]\) \(1382400\) \(2.9597\)  
10830.p2 10830p4 \([1, 0, 1, -11248768, -13887315694]\) \(3345930611358906241/165622259047500\) \(7791845090099858347500\) \([4]\) \(1382400\) \(2.9597\)  
10830.p3 10830p2 \([1, 0, 1, -11111588, -14257372462]\) \(3225005357698077121/8526675600\) \(401144965603203600\) \([2, 2]\) \(691200\) \(2.6131\)  
10830.p4 10830p1 \([1, 0, 1, -685908, -228577454]\) \(-758575480593601/40535043840\) \(-1907006848826423040\) \([2]\) \(345600\) \(2.2666\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 10830.2.a.p

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.