Properties

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

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

Elliptic curves in class 439569.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
439569.v1 439569v2 \([1, -1, 1, -43086920, -83679766842]\) \(104154702625/24649677\) \(2093593702341600472236093\) \([2]\) \(49545216\) \(3.3783\)  
439569.v2 439569v1 \([1, -1, 1, -14514935, 20185113030]\) \(3981876625/232713\) \(19765227400465363935417\) \([2]\) \(24772608\) \(3.0317\) \(\Gamma_0(N)\)-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.

Rank

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)
 
\(q - q^{2} - q^{4} - 2 q^{7} + 3 q^{8} + 2 q^{11} + 2 q^{14} - q^{16} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.