Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 930.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
930.n1 930n4 \([1, 0, 0, -635471, -195033699]\) \(28379906689597370652529/1357352437500\) \(1357352437500\) \([2]\) \(8640\) \(1.8053\)  
930.n2 930n3 \([1, 0, 0, -39651, -3060495]\) \(-6894246873502147249/47925198774000\) \(-47925198774000\) \([2]\) \(4320\) \(1.4587\)  
930.n3 930n2 \([1, 0, 0, -8531, -218655]\) \(68663623745397169/19216056254400\) \(19216056254400\) \([6]\) \(2880\) \(1.2560\)  
930.n4 930n1 \([1, 0, 0, 1389, -22239]\) \(296354077829711/387386634240\) \(-387386634240\) \([6]\) \(1440\) \(0.90944\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 930.2.a.n

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.