Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6930bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.bb4 6930bd1 \([1, -1, 1, 2308, -57409]\) \(1865864036231/2993760000\) \(-2182451040000\) \([4]\) \(10240\) \(1.0528\) \(\Gamma_0(N)\)-optimal
6930.bb3 6930bd2 \([1, -1, 1, -15692, -575809]\) \(586145095611769/140040608400\) \(102089603523600\) \([2, 2]\) \(20480\) \(1.3994\)  
6930.bb1 6930bd3 \([1, -1, 1, -234392, -43615969]\) \(1953542217204454969/170843779260\) \(124545115080540\) \([2]\) \(40960\) \(1.7459\)  
6930.bb2 6930bd4 \([1, -1, 1, -84992, 9070751]\) \(93137706732176569/5369647977540\) \(3914473375626660\) \([2]\) \(40960\) \(1.7459\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6930.2.a.bd

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