Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6930.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.ba1 6930t4 \([1, -1, 1, -69878, -7069463]\) \(1917114236485083/7117764500\) \(140098958653500\) \([2]\) \(41472\) \(1.5744\)  
6930.ba2 6930t2 \([1, -1, 1, -4538, 111161]\) \(382704614800227/27778076480\) \(750008064960\) \([6]\) \(13824\) \(1.0251\)  
6930.ba3 6930t3 \([1, -1, 1, -2378, -211463]\) \(-75526045083/943250000\) \(-18565989750000\) \([2]\) \(20736\) \(1.2278\)  
6930.ba4 6930t1 \([1, -1, 1, 262, 7481]\) \(73929353373/954060800\) \(-25759641600\) \([6]\) \(6912\) \(0.67848\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6930.2.a.ba

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.