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Properties

Label 462722g
Number of curves $3$
Conductor $462722$
CM no
Rank $1$
Graph

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

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 462722g have rank \(1\).

Complex multiplication

The elliptic curves in class 462722g do not have complex multiplication.

Modular form 462722.2.a.g

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 3 q^{5} - q^{6} + q^{7} - q^{8} - 2 q^{9} + 3 q^{10} - 6 q^{11} + q^{12} - q^{14} - 3 q^{15} + q^{16} + 3 q^{17} + 2 q^{18} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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 Cremona numbering.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 462722g

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
462722.g3 462722g1 \([1, 0, 1, 110860, 23322340]\) \(12167/26\) \(-321991054384970906\) \([]\) \(5624640\) \(2.0437\) \(\Gamma_0(N)\)-optimal
462722.g2 462722g2 \([1, 0, 1, -1045945, -820682588]\) \(-10218313/17576\) \(-217665952764240332456\) \([]\) \(16873920\) \(2.5930\)  
462722.g1 462722g3 \([1, 0, 1, -106315200, -421939810290]\) \(-10730978619193/6656\) \(-82429709922552551936\) \([]\) \(50621760\) \(3.1423\)