Properties

Label 67830.q
Number of curves $4$
Conductor $67830$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 67830.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
67830.q1 67830t4 \([1, 0, 1, -578294, 113832776]\) \(21387926929424202058969/6774718645013256000\) \(6774718645013256000\) \([2]\) \(1741824\) \(2.3172\)  
67830.q2 67830t2 \([1, 0, 1, -523979, 145944722]\) \(15909779688753017303209/1267090311060\) \(1267090311060\) \([6]\) \(580608\) \(1.7679\)  
67830.q3 67830t1 \([1, 0, 1, -32679, 2288602]\) \(-3859320826323964009/34671204111600\) \(-34671204111600\) \([6]\) \(290304\) \(1.4214\) \(\Gamma_0(N)\)-optimal
67830.q4 67830t3 \([1, 0, 1, 101706, 12104776]\) \(116350853426302261031/130543121856000000\) \(-130543121856000000\) \([2]\) \(870912\) \(1.9707\)  

Rank

sage: E.rank()
 

The elliptic curves in class 67830.q have rank \(1\).

Complex multiplication

The elliptic curves in class 67830.q do not have complex multiplication.

Modular form 67830.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + q^{10} - 6 q^{11} + q^{12} + 2 q^{13} - q^{14} - q^{15} + q^{16} + q^{17} - q^{18} + q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.