Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 10830.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10830.e1 10830e4 \([1, 1, 0, -167226398, -531563735292]\) \(10993009831928446009969/3767761230468750000\) \(177257646485046386718750000\) \([2]\) \(6220800\) \(3.7386\)  
10830.e2 10830e2 \([1, 1, 0, -149811758, -705838483788]\) \(7903870428425797297009/886464000000\) \(41704479854784000000\) \([2]\) \(2073600\) \(3.1893\)  
10830.e3 10830e1 \([1, 1, 0, -9339438, -11090483532]\) \(-1914980734749238129/20440940544000\) \(-961662056361099264000\) \([2]\) \(1036800\) \(2.8427\) \(\Gamma_0(N)\)-optimal
10830.e4 10830e3 \([1, 1, 0, 30861522, -57697813068]\) \(69096190760262356111/70568821500000000\) \(-3319972378599241500000000\) \([2]\) \(3110400\) \(3.3920\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 10830.2.a.e

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

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.