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Properties

Label 930.d
Number of curves $2$
Conductor $930$
CM no
Rank $1$
Graph

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

Elliptic curves in class 930.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
930.d1 930d2 \([1, 1, 0, -37442, 2585844]\) \(5805223604235668521/435937500000000\) \(435937500000000\) \([2]\) \(5376\) \(1.5544\)  
930.d2 930d1 \([1, 1, 0, 2238, 181236]\) \(1238798620042199/14760960000000\) \(-14760960000000\) \([2]\) \(2688\) \(1.2078\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 930.d have rank \(1\).

Complex multiplication

The elliptic curves in class 930.d do not have complex multiplication.

Modular form 930.2.a.d

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