Properties

Label 183150.cu
Number of curves $4$
Conductor $183150$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cu1")
 
E.isogeny_class()
 

Elliptic curves in class 183150.cu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
183150.cu1 183150ew4 \([1, -1, 0, -1261670967, -17248817857059]\) \(19499096390516434897995817/15393430272\) \(175340791692000000\) \([2]\) \(62914560\) \(3.5133\)  
183150.cu2 183150ew2 \([1, -1, 0, -78854967, -269494177059]\) \(4760617885089919932457/133756441657344\) \(1523569468253184000000\) \([2, 2]\) \(31457280\) \(3.1668\)  
183150.cu3 183150ew3 \([1, -1, 0, -75686967, -292142209059]\) \(-4209586785160189454377/801182513521564416\) \(-9125969568081569676000000\) \([2]\) \(62914560\) \(3.5133\)  
183150.cu4 183150ew1 \([1, -1, 0, -5126967, -3852193059]\) \(1308451928740468777/194033737531392\) \(2210165541568512000000\) \([2]\) \(15728640\) \(2.8202\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 183150.cu have rank \(0\).

Complex multiplication

The elliptic curves in class 183150.cu do not have complex multiplication.

Modular form 183150.2.a.cu

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