Properties

Label 384813g
Number of curves 2
Conductor 384813
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("384813.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 384813g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
384813.g2 384813g1 [1, -1, 1, -35015, 36681558] [2] 2949120 \(\Gamma_0(N)\)-optimal
384813.g1 384813g2 [1, -1, 1, -1883030, 987300474] [2] 5898240  

Rank

sage: E.rank()
 

The elliptic curves in class 384813g have rank \(1\).

Modular form 384813.2.a.g

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

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 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.