Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4830.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4830.s1 4830t3 \([1, 1, 1, -4491, -117711]\) \(10017490085065009/235066440\) \(235066440\) \([2]\) \(6144\) \(0.71829\)  
4830.s2 4830t4 \([1, 1, 1, -1211, 14033]\) \(196416765680689/22365315000\) \(22365315000\) \([2]\) \(6144\) \(0.71829\)  
4830.s3 4830t2 \([1, 1, 1, -291, -1791]\) \(2725812332209/373262400\) \(373262400\) \([2, 2]\) \(3072\) \(0.37171\)  
4830.s4 4830t1 \([1, 1, 1, 29, -127]\) \(2691419471/9891840\) \(-9891840\) \([2]\) \(1536\) \(0.025141\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4830.2.a.s

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.