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Properties

Label 273273g
Number of curves $2$
Conductor $273273$
CM no
Rank $0$
Graph

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

Elliptic curves in class 273273g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
273273.g2 273273g1 \([1, 1, 1, 2231557, 221882240]\) \(985074875/586971\) \(-732310153679247910767\) \([2]\) \(7907328\) \(2.6929\) \(\Gamma_0(N)\)-optimal
273273.g1 273273g2 \([1, 1, 1, -9072008, 1777252784]\) \(66184391125/37202781\) \(46414514978432331868137\) \([2]\) \(15814656\) \(3.0395\)  

Rank

sage: E.rank()
 

The elliptic curves in class 273273g have rank \(0\).

Complex multiplication

The elliptic curves in class 273273g do not have complex multiplication.

Modular form 273273.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + q^{6} + 3 q^{8} + q^{9} + q^{11} + q^{12} - q^{16} - 2 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.