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Properties

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

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 4830.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4830.i1 4830j3 \([1, 0, 1, -1844, 28292]\) \(692895692874169/51420783750\) \(51420783750\) \([2]\) \(6144\) \(0.80100\)  
4830.i2 4830j2 \([1, 0, 1, -374, -2284]\) \(5763259856089/1143116100\) \(1143116100\) \([2, 2]\) \(3072\) \(0.45443\)  
4830.i3 4830j1 \([1, 0, 1, -354, -2588]\) \(4886171981209/270480\) \(270480\) \([2]\) \(1536\) \(0.10786\) \(\Gamma_0(N)\)-optimal
4830.i4 4830j4 \([1, 0, 1, 776, -13324]\) \(51774168853511/107398242630\) \(-107398242630\) \([2]\) \(6144\) \(0.80100\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4830.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + q^{10} + 4 q^{11} + q^{12} + 2 q^{13} + q^{14} - q^{15} + q^{16} - 6 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.