Properties

Label 6930.x
Number of curves $4$
Conductor $6930$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6930.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.x1 6930bc4 \([1, -1, 1, -188183, 31467871]\) \(1010962818911303721/57392720\) \(41839292880\) \([2]\) \(32768\) \(1.5047\)  
6930.x2 6930bc3 \([1, -1, 1, -19703, -246113]\) \(1160306142246441/634128110000\) \(462279392190000\) \([2]\) \(32768\) \(1.5047\)  
6930.x3 6930bc2 \([1, -1, 1, -11783, 492031]\) \(248158561089321/1859334400\) \(1355454777600\) \([2, 2]\) \(16384\) \(1.1581\)  
6930.x4 6930bc1 \([1, -1, 1, -263, 17407]\) \(-2749884201/176619520\) \(-128755630080\) \([2]\) \(8192\) \(0.81155\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6930.x have rank \(1\).

Complex multiplication

The elliptic curves in class 6930.x do not have complex multiplication.

Modular form 6930.2.a.x

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.