Properties

Label 440818.w
Number of curves $2$
Conductor $440818$
CM no
Rank $0$
Graph

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

Elliptic curves in class 440818.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
440818.w1 440818w2 \([1, 0, 0, -466705134, -3880749124084]\) \(2337944550222313/4769464\) \(22934370055209523762936\) \([]\) \(152295552\) \(3.5410\)  
440818.w2 440818w1 \([1, 0, 0, -7535689, -1777486613]\) \(9841819033/5411854\) \(26023356570207025782046\) \([]\) \(50765184\) \(2.9917\) \(\Gamma_0(N)\)-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 440818.w1.

Rank

sage: E.rank()
 

The elliptic curves in class 440818.w have rank \(0\).

Complex multiplication

The elliptic curves in class 440818.w do not have complex multiplication.

Modular form 440818.2.a.w

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + 3 q^{5} + q^{6} + q^{7} + q^{8} - 2 q^{9} + 3 q^{10} + 6 q^{11} + q^{12} + 4 q^{13} + q^{14} + 3 q^{15} + q^{16} + 6 q^{17} - 2 q^{18} - 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.