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Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 439569.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
439569.w1 439569w1 [1, -1, 1, -35015, -1757154] [2] 1769472 \(\Gamma_0(N)\)-optimal
439569.w2 439569w2 [1, -1, 1, 94270, -11789670] [2] 3538944  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 439569.2.a.w

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

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.