Properties

Label 78400gy
Number of curves $4$
Conductor $78400$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("78400.gq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 78400gy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
78400.gq4 78400gy1 [0, 0, 0, 181300, -47334000] [2] 884736 \(\Gamma_0(N)\)-optimal
78400.gq3 78400gy2 [0, 0, 0, -1386700, -508326000] [2, 2] 1769472  
78400.gq2 78400gy3 [0, 0, 0, -6874700, 6483386000] [2] 3538944  
78400.gq1 78400gy4 [0, 0, 0, -20986700, -37003526000] [2] 3538944  

Rank

sage: E.rank()
 

The elliptic curves in class 78400gy have rank \(1\).

Modular form 78400.2.a.gq

sage: E.q_eigenform(10)
 
\( q - 3q^{9} + 4q^{11} + 6q^{13} + 2q^{17} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.