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Properties

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

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 10830.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.w1 10830y4 \([1, 1, 1, -349275, 79289397]\) \(100162392144121/23457780\) \(1103591926404180\) \([2]\) \(184320\) \(1.8769\)  
10830.w2 10830y3 \([1, 1, 1, -161555, -24372475]\) \(9912050027641/311647500\) \(14661731198947500\) \([2]\) \(184320\) \(1.8769\)  
10830.w3 10830y2 \([1, 1, 1, -24375, 923517]\) \(34043726521/11696400\) \(550267442528400\) \([2, 2]\) \(92160\) \(1.5303\)  
10830.w4 10830y1 \([1, 1, 1, 4505, 103325]\) \(214921799/218880\) \(-10297402433280\) \([4]\) \(46080\) \(1.1838\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 10830.2.a.w

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