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Properties

Label 439824.gb
Number of curves $2$
Conductor $439824$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("gb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 439824.gb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
439824.gb1 439824gb1 [0, 1, 0, -708752, 227610900] [2] 7741440 \(\Gamma_0(N)\)-optimal
439824.gb2 439824gb2 [0, 1, 0, -206992, 544121108] [2] 15482880  

Rank

sage: E.rank()
 

The elliptic curves in class 439824.gb have rank \(0\).

Complex multiplication

The elliptic curves in class 439824.gb do not have complex multiplication.

Modular form 439824.2.a.gb

sage: E.q_eigenform(10)
 
\( q + q^{3} + 2q^{5} + q^{9} + q^{11} + 4q^{13} + 2q^{15} + q^{17} - 8q^{19} + O(q^{20}) \)

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 LMFDB 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 LMFDB labels.