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Properties

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

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 440818i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
440818.i2 440818i1 \([1, 0, 1, -5505, -35538]\) \(9841819033/5411854\) \(10142685704494\) \([3]\) \(1372032\) \(1.1863\) \(\Gamma_0(N)\)-optimal
440818.i1 440818i2 \([1, 0, 1, -340910, -76642040]\) \(2337944550222313/4769464\) \(8938743419704\) \([]\) \(4116096\) \(1.7356\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 440818.2.a.i

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 Cremona 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 Cremona labels.