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Properties

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

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 32490.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32490.l1 32490g2 \([1, -1, 0, -195549, -32914395]\) \(651038076963/7220000\) \(9171124042140000\) \([2]\) \(460800\) \(1.8772\)  
32490.l2 32490g1 \([1, -1, 0, -22269, 459333]\) \(961504803/486400\) \(617844145996800\) \([2]\) \(230400\) \(1.5307\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 32490.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - 4 q^{7} - q^{8} - q^{10} - 6 q^{11} + 4 q^{14} + q^{16} + 4 q^{17} + O(q^{20})\) 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 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.