Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("930.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 930.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
930.g1 930g3 [1, 0, 1, -1514, -21814] [2] 1152  
930.g2 930g2 [1, 0, 1, -264, 1186] [2, 2] 576  
930.g3 930g1 [1, 0, 1, -244, 1442] [2] 288 \(\Gamma_0(N)\)-optimal
930.g4 930g4 [1, 0, 1, 666, 7882] [2] 1152  

Rank

sage: E.rank()
 

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

Modular form 930.2.a.g

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.