Properties

Label 32490.w
Number of curves $2$
Conductor $32490$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 32490.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32490.w1 32490q2 \([1, -1, 0, -32814, 2296120]\) \(781484460931/900\) \(4500189900\) \([2]\) \(61440\) \(1.1363\)  
32490.w2 32490q1 \([1, -1, 0, -2034, 36868]\) \(-186169411/6480\) \(-32401367280\) \([2]\) \(30720\) \(0.78973\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 32490.w have rank \(1\).

Complex multiplication

The elliptic curves in class 32490.w do not have complex multiplication.

Modular form 32490.2.a.w

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} + 2 q^{7} - q^{8} - q^{10} - 2 q^{13} - 2 q^{14} + q^{16} + 6 q^{17} + O(q^{20})\)  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.