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Properties

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

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 273273.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
273273.u1 273273u2 \([1, 0, 0, -196711187, 1061898796230]\) \(674733819141829/3361743\) \(4194139971072056216211\) \([2]\) \(38817792\) \(3.3479\)  
273273.u2 273273u1 \([1, 0, 0, -12086292, 17180365383]\) \(-156503678869/11647251\) \(-14531212223007225072327\) \([2]\) \(19408896\) \(3.0013\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 273273.2.a.u

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