Properties

Label 439569.q
Number of curves $2$
Conductor $439569$
CM no
Rank $0$
Graph

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

Elliptic curves in class 439569.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
439569.q1 439569q2 [1, -1, 1, -32976833, 405266116610] [] 76876800 \(\Gamma_0(N)\)-optimal*
439569.q2 439569q1 [1, -1, 1, -4404848, -3598988740] [] 10982400 \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 439569.q1.

Rank

sage: E.rank()
 

The elliptic curves in class 439569.q have rank \(0\).

Complex multiplication

The elliptic curves in class 439569.q do not have complex multiplication.

Modular form 439569.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - q^{5} - 2q^{7} + 3q^{8} + q^{10} - 2q^{11} + 2q^{14} - q^{16} - 6q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.