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Properties

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

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 4830.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4830.d1 4830d2 \([1, 1, 0, -948, -11592]\) \(94376601570889/456435000\) \(456435000\) \([2]\) \(3072\) \(0.51012\)  
4830.d2 4830d1 \([1, 1, 0, -28, -368]\) \(-2565726409/53323200\) \(-53323200\) \([2]\) \(1536\) \(0.16354\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4830.2.a.d

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