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

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Show commands for: SageMath
sage: E = EllipticCurve("v1")
sage: E.isogeny_class()

Elliptic curves in class 439569.v

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
439569.v1 439569v2 [1, -1, 1, -43086920, -83679766842] [2] 49545216  
439569.v2 439569v1 [1, -1, 1, -14514935, 20185113030] [2] 24772608 \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 439569.v1.


sage: E.rank()

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

Complex multiplication

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

Modular form 439569.2.a.v

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

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.