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Properties

Label 4730.k
Number of curves $2$
Conductor $4730$
CM no
Rank $0$
Graph

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

Elliptic curves in class 4730.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4730.k1 4730i2 \([1, 1, 1, -43087000, 71076326617]\) \(8846316694484611683132528001/2935896911621093750000000\) \(2935896911621093750000000\) \([2]\) \(850080\) \(3.3977\)  
4730.k2 4730i1 \([1, 1, 1, 7797480, 7653910745]\) \(52430803961239418232136319/55627994831200000000000\) \(-55627994831200000000000\) \([2]\) \(425040\) \(3.0511\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4730.k have rank \(0\).

Complex multiplication

The elliptic curves in class 4730.k do not have complex multiplication.

Modular form 4730.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} + q^{4} + q^{5} + 2 q^{6} + q^{8} + q^{9} + q^{10} + q^{11} + 2 q^{12} + 6 q^{13} + 2 q^{15} + q^{16} + 2 q^{17} + q^{18} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.