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Properties

Label 6930d
Number of curves $2$
Conductor $6930$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 6930d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.k1 6930d1 \([1, -1, 0, -2364, 44828]\) \(74246873427/16940\) \(333430020\) \([2]\) \(6144\) \(0.62720\) \(\Gamma_0(N)\)-optimal
6930.k2 6930d2 \([1, -1, 0, -2094, 55250]\) \(-51603494067/35870450\) \(-706038067350\) \([2]\) \(12288\) \(0.97377\)  

Rank

sage: E.rank()
 

The elliptic curves in class 6930d have rank \(1\).

Complex multiplication

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

Modular form 6930.2.a.d

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