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Properties

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

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 440818x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
440818.x2 440818x1 \([1, 1, 1, -4892150, 4468286131]\) \(-5046760173468889/444161163712\) \(-1139596027588050870208\) \([2]\) \(53581824\) \(2.7843\) \(\Gamma_0(N)\)-optimal*
440818.x1 440818x2 \([1, 1, 1, -79858590, 274647335891]\) \(21952211680680400729/150176112968\) \(385310819042964971912\) \([2]\) \(107163648\) \(3.1309\) \(\Gamma_0(N)\)-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 440818x1.

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 440818.2.a.x

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