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Properties

Label 440818o
Number of curves $3$
Conductor $440818$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 440818o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
440818.o3 440818o1 \([1, 0, 0, 113132078, -933569647764]\) \(62412367968676722023/182867427413015464\) \(-469187787859464326310188776\) \([]\) \(253528704\) \(3.8012\) \(\Gamma_0(N)\)-optimal
440818.o2 440818o2 \([1, 0, 0, -4967137937, -135024131935319]\) \(-5282409060555942439635337/12733300881458665984\) \(-32670166345301477757058771456\) \([]\) \(760586112\) \(4.3505\)  
440818.o1 440818o3 \([1, 0, 0, -402570647352, -98313106857612224]\) \(-2812157792529125619433313717497/39177215279104\) \(-100518015872675438657536\) \([]\) \(2281758336\) \(4.8998\)  

Rank

sage: E.rank()
 

The elliptic curves in class 440818o have rank \(1\).

Complex multiplication

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

Modular form 440818.2.a.o

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.