Properties

Label 32490e
Number of curves $2$
Conductor $32490$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 32490e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32490.u2 32490e1 \([1, -1, 0, -1509079884, -22563511512112]\) \(59839327109608353/400000000\) \(2540584782153622800000000\) \([2]\) \(14592000\) \(3.8650\) \(\Gamma_0(N)\)-optimal
32490.u1 32490e2 \([1, -1, 0, -1538710764, -21631282544080]\) \(63433837731204513/4882812500000\) \(31012997829023715820312500000\) \([2]\) \(29184000\) \(4.2116\)  

Rank

sage: E.rank()
 

The elliptic curves in class 32490e have rank \(0\).

Complex multiplication

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

Modular form 32490.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} - 4 q^{11} - 2 q^{13} + q^{16} + 4 q^{17} + O(q^{20})\) 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.