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Properties

Label 32490a
Number of curves $2$
Conductor $32490$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 32490a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32490.h2 32490a1 \([1, -1, 0, -464475, -121723739]\) \(59839327109608353/400000000\) \(74077200000000\) \([2]\) \(256000\) \(1.8435\) \(\Gamma_0(N)\)-optimal
32490.h1 32490a2 \([1, -1, 0, -473595, -116687675]\) \(63433837731204513/4882812500000\) \(904262695312500000\) \([2]\) \(512000\) \(2.1900\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 32490.2.a.a

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.