Properties

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

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

Elliptic curves in class 930o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
930.o6 930o1 \([1, 0, 0, 60, -1008]\) \(23862997439/457113600\) \(-457113600\) \([4]\) \(512\) \(0.34210\) \(\Gamma_0(N)\)-optimal
930.o5 930o2 \([1, 0, 0, -1220, -15600]\) \(200828550012481/12454560000\) \(12454560000\) \([2, 4]\) \(1024\) \(0.68868\)  
930.o2 930o3 \([1, 0, 0, -19220, -1027200]\) \(785209010066844481/3324675600\) \(3324675600\) \([2, 2]\) \(2048\) \(1.0353\)  
930.o4 930o4 \([1, 0, 0, -3700, 67232]\) \(5601911201812801/1271193750000\) \(1271193750000\) \([8]\) \(2048\) \(1.0353\)  
930.o1 930o5 \([1, 0, 0, -307520, -65664060]\) \(3216206300355197383681/57660\) \(57660\) \([2]\) \(4096\) \(1.3818\)  
930.o3 930o6 \([1, 0, 0, -18920, -1060740]\) \(-749011598724977281/51173462246460\) \(-51173462246460\) \([2]\) \(4096\) \(1.3818\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 930.2.a.o

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.