Properties

Label 6930.g
Number of curves $2$
Conductor $6930$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6930.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.g1 6930j1 \([1, -1, 0, -44955, 3679825]\) \(13782741913468081/701662500\) \(511511962500\) \([2]\) \(23040\) \(1.3167\) \(\Gamma_0(N)\)-optimal
6930.g2 6930j2 \([1, -1, 0, -42525, 4093411]\) \(-11666347147400401/3126621093750\) \(-2279306777343750\) \([2]\) \(46080\) \(1.6633\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6930.2.a.g

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.