Properties

Label 494508q
Number of curves $2$
Conductor $494508$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 494508q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
494508.q2 494508q1 \([0, -1, 0, -384617, 76036710]\) \(16384/3\) \(1152156793443304656\) \([2]\) \(7526400\) \(2.1842\) \(\Gamma_0(N)\)-optimal
494508.q1 494508q2 \([0, -1, 0, -1826932, -879929672]\) \(109744/9\) \(55303526085278623488\) \([2]\) \(15052800\) \(2.5308\)  

Rank

sage: E.rank()
 

The elliptic curves in class 494508q have rank \(1\).

Complex multiplication

The elliptic curves in class 494508q do not have complex multiplication.

Modular form 494508.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{5} + q^{9} - 2 q^{11} - 4 q^{13} - 2 q^{15} - 6 q^{17} - 8 q^{19} + O(q^{20})\) 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.