Properties

Label 6930.bc
Number of curves $4$
Conductor $6930$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6930.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.bc1 6930be3 \([1, -1, 1, -26916647, -53548383009]\) \(2958414657792917260183849/12401051653985258880\) \(9040366655755253723520\) \([2]\) \(802816\) \(3.0677\)  
6930.bc2 6930be2 \([1, -1, 1, -2523047, 88264671]\) \(2436531580079063806249/1405478914998681600\) \(1024594129034038886400\) \([2, 2]\) \(401408\) \(2.7211\)  
6930.bc3 6930be1 \([1, -1, 1, -1785767, 916672479]\) \(863913648706111516969/2486234429521920\) \(1812464899121479680\) \([4]\) \(200704\) \(2.3745\) \(\Gamma_0(N)\)-optimal
6930.bc4 6930be4 \([1, -1, 1, 10074073, 697965279]\) \(155099895405729262880471/90047655797243760000\) \(-65644741076190701040000\) \([2]\) \(802816\) \(3.0677\)  

Rank

sage: E.rank()
 

The elliptic curves in class 6930.bc have rank \(0\).

Complex multiplication

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

Modular form 6930.2.a.bc

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.