Properties

Label 930g
Number of curves $4$
Conductor $930$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 930g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
930.g3 930g1 \([1, 0, 1, -244, 1442]\) \(1597099875769/186000\) \(186000\) \([2]\) \(288\) \(0.037436\) \(\Gamma_0(N)\)-optimal
930.g2 930g2 \([1, 0, 1, -264, 1186]\) \(2023804595449/540562500\) \(540562500\) \([2, 2]\) \(576\) \(0.38401\)  
930.g1 930g3 \([1, 0, 1, -1514, -21814]\) \(383432500775449/18701300250\) \(18701300250\) \([2]\) \(1152\) \(0.73058\)  
930.g4 930g4 \([1, 0, 1, 666, 7882]\) \(32740359775271/45410156250\) \(-45410156250\) \([2]\) \(1152\) \(0.73058\)  

Rank

sage: E.rank()
 

The elliptic curves in class 930g have rank \(0\).

Complex multiplication

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

Modular form 930.2.a.g

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