Properties

Label 81144.y
Number of curves $2$
Conductor $81144$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 81144.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
81144.y1 81144bn2 \([0, 0, 0, -215355, 38463334]\) \(12576878500/1127\) \(98978220407808\) \([2]\) \(368640\) \(1.7255\)  
81144.y2 81144bn1 \([0, 0, 0, -12495, 690802]\) \(-9826000/3703\) \(-81303538192128\) \([2]\) \(184320\) \(1.3789\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 81144.y have rank \(2\).

Complex multiplication

The elliptic curves in class 81144.y do not have complex multiplication.

Modular form 81144.2.a.y

sage: E.q_eigenform(10)
 
\(q - 4 q^{11} - 6 q^{13} + O(q^{20})\) 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.