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Properties

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

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

Elliptic curves in class 320790.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
320790.f1 320790f4 \([1, 1, 0, -3030893, -907847907]\) \(127568139540190201/59114336463360\) \(1426876375273567971840\) \([2]\) \(27869184\) \(2.7537\)  
320790.f2 320790f2 \([1, 1, 0, -1535318, 731549388]\) \(16581570075765001/998001000\) \(24089317999569000\) \([2]\) \(9289728\) \(2.2044\)  
320790.f3 320790f1 \([1, 1, 0, -90318, 12806388]\) \(-3375675045001/999000000\) \(-24113431431000000\) \([2]\) \(4644864\) \(1.8579\) \(\Gamma_0(N)\)-optimal
320790.f4 320790f3 \([1, 1, 0, 668307, -106601187]\) \(1367594037332999/995878502400\) \(-24038086067296665600\) \([2]\) \(13934592\) \(2.4072\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 320790.2.a.f

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