Properties

Label 116380e
Number of curves 4
Conductor 116380
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("116380.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116380e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
116380.a4 116380e1 [0, 1, 0, -23981, -1408100] [2] 427680 \(\Gamma_0(N)\)-optimal
116380.a3 116380e2 [0, 1, 0, -53076, 2641924] [2] 855360  
116380.a2 116380e3 [0, 1, 0, -235581, 43377040] [2] 1283040  
116380.a1 116380e4 [0, 1, 0, -3756076, 2800628724] [2] 2566080  

Rank

sage: E.rank()
 

The elliptic curves in class 116380e have rank \(0\).

Modular form 116380.2.a.a

sage: E.q_eigenform(10)
 
\( q - 2q^{3} - q^{5} + 4q^{7} + q^{9} + q^{11} - 4q^{13} + 2q^{15} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.