Properties

Label 439569bb
Number of curves $2$
Conductor $439569$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 439569bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
439569.bb2 439569bb1 [1, -1, 1, -539, 139026] [2] 688128 \(\Gamma_0(N)\)-optimal*
439569.bb1 439569bb2 [1, -1, 1, -43634, 3483198] [2] 1376256 \(\Gamma_0(N)\)-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 439569bb1.

Rank

sage: E.rank()
 

The elliptic curves in class 439569bb have rank \(1\).

Complex multiplication

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

Modular form 439569.2.a.bb

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

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 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.