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Properties

Label 84150ga
Number of curves $2$
Conductor $84150$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ga1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 84150ga

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
84150.gi2 84150ga1 [1, -1, 1, -2705, -43203] [2] 98304 \(\Gamma_0(N)\)-optimal
84150.gi1 84150ga2 [1, -1, 1, -40955, -3179703] [2] 196608  

Rank

sage: E.rank()
 

The elliptic curves in class 84150ga have rank \(1\).

Complex multiplication

The elliptic curves in class 84150ga do not have complex multiplication.

Modular form 84150.2.a.ga

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + 2q^{7} + q^{8} + q^{11} - 4q^{13} + 2q^{14} + q^{16} + q^{17} + 2q^{19} + O(q^{20}) \)

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.