Properties

Label 4830.u
Number of curves $2$
Conductor $4830$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4830.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4830.u1 4830u1 \([1, 1, 1, -112286, 14435483]\) \(156567200830221067489/16905000000\) \(16905000000\) \([2]\) \(17472\) \(1.3894\) \(\Gamma_0(N)\)-optimal
4830.u2 4830u2 \([1, 1, 1, -112006, 14511419]\) \(-155398856216042825569/1627294921875000\) \(-1627294921875000\) \([2]\) \(34944\) \(1.7360\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4830.u have rank \(0\).

Complex multiplication

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

Modular form 4830.2.a.u

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.