Properties

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

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 440818c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
440818.c2 440818c1 \([1, 0, 1, -806, -82824]\) \(-42223146625/2136719872\) \(-2925169504768\) \([]\) \(878688\) \(1.0720\) \(\Gamma_0(N)\)-optimal
440818.c1 440818c2 \([1, 0, 1, -171006, -27233128]\) \(-403971436666266625/7425063688\) \(-10164912188872\) \([]\) \(2636064\) \(1.6213\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 440818.2.a.c

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