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Properties

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

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 4830.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4830.e1 4830e1 \([1, 1, 0, -119387, 15827229]\) \(188191720927962271801/9422571110400\) \(9422571110400\) \([2]\) \(27648\) \(1.5604\) \(\Gamma_0(N)\)-optimal
4830.e2 4830e2 \([1, 1, 0, -112987, 17607709]\) \(-159520003524722950201/42335913815758080\) \(-42335913815758080\) \([2]\) \(55296\) \(1.9070\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4830.2.a.e

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.