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

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Show commands for: SageMath
sage: E = EllipticCurve("u1")
sage: E.isogeny_class()

Elliptic curves in class 439569u

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
439569.u2 439569u1 [1, -1, 1, 24655, 1524696] [2] 1769472 \(\Gamma_0(N)\)-optimal*
439569.u1 439569u2 [1, -1, 1, -144410, 14644140] [2] 3538944 \(\Gamma_0(N)\)-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 439569u1.


sage: E.rank()

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

Complex multiplication

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

Modular form 439569.2.a.u

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

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.