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Properties

Label 27930.v
Number of curves $4$
Conductor $27930$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 27930.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
27930.v1 27930x4 \([1, 1, 0, -3476477, -2496371751]\) \(39496057701398850889/7068165300\) \(831562579379700\) \([2]\) \(589824\) \(2.2587\)  
27930.v2 27930x2 \([1, 1, 0, -217977, -38811051]\) \(9735776569434889/128952810000\) \(15171169143690000\) \([2, 2]\) \(294912\) \(1.9122\)  
27930.v3 27930x3 \([1, 1, 0, -32757, -102415599]\) \(-33042169120969/38485420312500\) \(-4527771214345312500\) \([4]\) \(589824\) \(2.2587\)  
27930.v4 27930x1 \([1, 1, 0, -25897, 642181]\) \(16327137318409/7882963200\) \(927422737516800\) \([2]\) \(147456\) \(1.5656\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 27930.v have rank \(0\).

Complex multiplication

The elliptic curves in class 27930.v do not have complex multiplication.

Modular form 27930.2.a.v

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.