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Properties

Label 272090d
Number of curves $2$
Conductor $272090$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 272090d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
272090.d2 272090d1 \([1, 0, 1, -1541284, 705706146]\) \(83890194895342081/3958384640000\) \(19106366605813760000\) \([2]\) \(9676800\) \(2.4604\) \(\Gamma_0(N)\)-optimal
272090.d1 272090d2 \([1, 0, 1, -4245284, -2448239454]\) \(1753007192038126081/478174101507200\) \(2308055056721866524800\) \([2]\) \(19353600\) \(2.8070\)  

Rank

sage: E.rank()
 

The elliptic curves in class 272090d have rank \(0\).

Complex multiplication

The elliptic curves in class 272090d do not have complex multiplication.

Modular form 272090.2.a.d

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