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Properties

Label 44286o
Number of curves $2$
Conductor $44286$
CM no
Rank $1$
Graph

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

Elliptic curves in class 44286o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44286.s2 44286o1 \([1, 0, 1, -608, -44530]\) \(-13997521/474336\) \(-840315158496\) \([]\) \(84000\) \(0.96839\) \(\Gamma_0(N)\)-optimal
44286.s1 44286o2 \([1, 0, 1, -62318, 7520390]\) \(-15107691357361/5067577806\) \(-8977523205575166\) \([]\) \(420000\) \(1.7731\)  

Rank

sage: E.rank()
 

The elliptic curves in class 44286o have rank \(1\).

Complex multiplication

The elliptic curves in class 44286o do not have complex multiplication.

Modular form 44286.2.a.o

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.