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Properties

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

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 440818q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
440818.q2 440818q1 \([1, 0, 0, -1102758, -4191963164]\) \(-42223146625/2136719872\) \(-7505184649184709018112\) \([3]\) \(32511456\) \(2.8774\) \(\Gamma_0(N)\)-optimal
440818.q1 440818q2 \([1, 0, 0, -234106558, -1378737300276]\) \(-403971436666266625/7425063688\) \(-26080383648154886320648\) \([]\) \(97534368\) \(3.4267\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 440818.2.a.q

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.