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Properties

Label 320790.g
Number of curves $4$
Conductor $320790$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 320790.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
320790.g1 320790g4 \([1, 1, 0, -92612512, -70662535496]\) \(3639478711331685826729/2016912141902025000\) \(48683355992097919677225000\) \([2]\) \(117964800\) \(3.6194\)  
320790.g2 320790g2 \([1, 1, 0, -56487512, 162423189504]\) \(825824067562227826729/5613755625000000\) \(135502413747575625000000\) \([2, 2]\) \(58982400\) \(3.2728\)  
320790.g3 320790g1 \([1, 1, 0, -56395032, 162984672576]\) \(821774646379511057449/38361600000\) \(925955766950400000\) \([2]\) \(29491200\) \(2.9263\) \(\Gamma_0(N)\)-optimal
320790.g4 320790g3 \([1, 1, 0, -21842192, 359575847496]\) \(-47744008200656797609/2286529541015625000\) \(-55191264566802978515625000\) \([2]\) \(117964800\) \(3.6194\)  

Rank

sage: E.rank()
 

The elliptic curves in class 320790.g have rank \(1\).

Complex multiplication

The elliptic curves in class 320790.g do not have complex multiplication.

Modular form 320790.2.a.g

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