Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6930.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.f1 6930h4 \([1, -1, 0, -31680, 2166426]\) \(4823468134087681/30382271150\) \(22148675668350\) \([6]\) \(27648\) \(1.3981\)  
6930.f2 6930h2 \([1, -1, 0, -2430, -43524]\) \(2177286259681/105875000\) \(77182875000\) \([2]\) \(9216\) \(0.84882\)  
6930.f3 6930h3 \([1, -1, 0, -810, 73440]\) \(-80677568161/3131816380\) \(-2283094141020\) \([6]\) \(13824\) \(1.0515\)  
6930.f4 6930h1 \([1, -1, 0, 90, -2700]\) \(109902239/4312000\) \(-3143448000\) \([2]\) \(4608\) \(0.50224\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 6930.2.a.f

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

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.