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Properties

Label 4830.z
Number of curves $4$
Conductor $4830$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 4830.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4830.z1 4830y4 \([1, 1, 1, -36920100, 86327581317]\) \(5565604209893236690185614401/229307220930246900000\) \(229307220930246900000\) \([2]\) \(614400\) \(2.9882\)  
4830.z2 4830y3 \([1, 1, 1, -11255780, -13408567675]\) \(157706830105239346386477121/13650704956054687500000\) \(13650704956054687500000\) \([2]\) \(614400\) \(2.9882\)  
4830.z3 4830y2 \([1, 1, 1, -2420100, 1209181317]\) \(1567558142704512417614401/274462175610000000000\) \(274462175610000000000\) \([2, 2]\) \(307200\) \(2.6416\)  
4830.z4 4830y1 \([1, 1, 1, 288380, 108455045]\) \(2652277923951208297919/6605028468326400000\) \(-6605028468326400000\) \([4]\) \(153600\) \(2.2950\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4830.z have rank \(1\).

Complex multiplication

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

Modular form 4830.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{7} + q^{8} + q^{9} + q^{10} - q^{12} - 6 q^{13} + q^{14} - q^{15} + q^{16} - 6 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.