Properties

Label 930.o
Number of curves $6$
Conductor $930$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("930.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 930.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
930.o1 930o5 [1, 0, 0, -307520, -65664060] [2] 4096  
930.o2 930o3 [1, 0, 0, -19220, -1027200] [2, 2] 2048  
930.o3 930o6 [1, 0, 0, -18920, -1060740] [2] 4096  
930.o4 930o4 [1, 0, 0, -3700, 67232] [8] 2048  
930.o5 930o2 [1, 0, 0, -1220, -15600] [2, 4] 1024  
930.o6 930o1 [1, 0, 0, 60, -1008] [4] 512 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 930.2.a.o

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.