Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("bi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6930.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.bi1 6930bm3 \([1, -1, 1, -7772, 263621]\) \(71210194441849/631496250\) \(460360766250\) \([2]\) \(16384\) \(1.0612\)  
6930.bi2 6930bm2 \([1, -1, 1, -842, -2491]\) \(90458382169/48024900\) \(35010152100\) \([2, 2]\) \(8192\) \(0.71467\)  
6930.bi3 6930bm1 \([1, -1, 1, -662, -6379]\) \(43949604889/55440\) \(40415760\) \([2]\) \(4096\) \(0.36810\) \(\Gamma_0(N)\)-optimal
6930.bi4 6930bm4 \([1, -1, 1, 3208, -21931]\) \(5009866738631/3163773690\) \(-2306391020010\) \([2]\) \(16384\) \(1.0612\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6930.2.a.bi

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.