Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 440818bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
440818.bb2 440818bb1 \([1, 1, 1, 47202, 18587099]\) \(4533086375/60669952\) \(-155662498079162368\) \([2]\) \(5806080\) \(1.9796\) \(\Gamma_0(N)\)-optimal*
440818.bb1 440818bb2 \([1, 1, 1, -828958, 271622107]\) \(24553362849625/1755162752\) \(4503267424899517568\) \([2]\) \(11612160\) \(2.3262\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 440818bb1.

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 440818.2.a.bb

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.