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Properties

Label 140790.a
Number of curves $4$
Conductor $140790$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 140790.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
140790.a1 140790cq4 \([1, 1, 0, -44311313, -103840874583]\) \(204524800857359188129/19379962604437500\) \(911747414472816696937500\) \([2]\) \(29859840\) \(3.3355\)  
140790.a2 140790cq2 \([1, 1, 0, -43249973, -109496027667]\) \(190177723376764332769/202737600\) \(9537969003825600\) \([2]\) \(9953280\) \(2.7862\)  
140790.a3 140790cq1 \([1, 1, 0, -2702453, -1712610003]\) \(-46395601158168289/47939973120\) \(-2255378270546718720\) \([2]\) \(4976640\) \(2.4396\) \(\Gamma_0(N)\)-optimal
140790.a4 140790cq3 \([1, 1, 0, 3275707, -7724611587]\) \(82626060291589151/595927492758000\) \(-28035933908921229798000\) \([2]\) \(14929920\) \(2.9889\)  

Rank

sage: E.rank()
 

The elliptic curves in class 140790.a have rank \(0\).

Complex multiplication

The elliptic curves in class 140790.a do not have complex multiplication.

Modular form 140790.2.a.a

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.