Properties

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

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 6930a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.c1 6930a1 \([1, -1, 0, -188340, -31409200]\) \(37537160298467283/5519360000\) \(108637562880000\) \([2]\) \(43008\) \(1.7075\) \(\Gamma_0(N)\)-optimal
6930.c2 6930a2 \([1, -1, 0, -171060, -37419184]\) \(-28124139978713043/14526050000000\) \(-285916242150000000\) \([2]\) \(86016\) \(2.0541\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6930.2.a.a

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.