Properties

Label 4830.q
Number of curves $2$
Conductor $4830$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4830.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4830.q1 4830p2 \([1, 0, 1, -423, 1828]\) \(8341959848041/3327411150\) \(3327411150\) \([2]\) \(3840\) \(0.52532\)  
4830.q2 4830p1 \([1, 0, 1, -193, -1024]\) \(789145184521/17996580\) \(17996580\) \([2]\) \(1920\) \(0.17875\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4830.2.a.q

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.