Properties

Label 4830b
Number of curves $4$
Conductor $4830$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 4830b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4830.b3 4830b1 \([1, 1, 0, -56723, -5223507]\) \(20184279492242626489/11148103680\) \(11148103680\) \([2]\) \(18432\) \(1.2556\) \(\Gamma_0(N)\)-optimal
4830.b2 4830b2 \([1, 1, 0, -57043, -5162003]\) \(20527812941011798969/474091398849600\) \(474091398849600\) \([2, 2]\) \(36864\) \(1.6022\)  
4830.b1 4830b3 \([1, 1, 0, -125643, 9559557]\) \(219353215817909485369/87028564162480920\) \(87028564162480920\) \([2]\) \(73728\) \(1.9487\)  
4830.b4 4830b4 \([1, 1, 0, 6437, -15940907]\) \(29489595518609351/109830613939935000\) \(-109830613939935000\) \([2]\) \(73728\) \(1.9487\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4830.2.a.b

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