Properties

Label 4830.n
Number of curves $4$
Conductor $4830$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 4830.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4830.n1 4830n3 \([1, 0, 1, -841301318, -9392446043944]\) \(65853432878493908038433301506521/38511703125000000\) \(38511703125000000\) \([2]\) \(1290240\) \(3.4077\)  
4830.n2 4830n2 \([1, 0, 1, -52581638, -146758467112]\) \(16077778198622525072705635801/388799208512064000000\) \(388799208512064000000\) \([2, 2]\) \(645120\) \(3.0612\)  
4830.n3 4830n4 \([1, 0, 1, -50621638, -158203299112]\) \(-14346048055032350809895395801/2509530875136386550792000\) \(-2509530875136386550792000\) \([4]\) \(1290240\) \(3.4077\)  
4830.n4 4830n1 \([1, 0, 1, -3409158, -2112699944]\) \(4381924769947287308715481/608122186185572352000\) \(608122186185572352000\) \([2]\) \(322560\) \(2.7146\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4830.n have rank \(0\).

Complex multiplication

The elliptic curves in class 4830.n do not have complex multiplication.

Modular form 4830.2.a.n

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.