Properties

Label 380880ex
Number of curves $6$
Conductor $380880$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("380880.ex1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 380880ex

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
380880.ex5 380880ex1 [0, 0, 0, -31995507, -76424358094] [2] 38928384 \(\Gamma_0(N)\)-optimal
380880.ex4 380880ex2 [0, 0, 0, -525615987, -4638168661966] [2, 2] 77856768  
380880.ex3 380880ex3 [0, 0, 0, -539327667, -4383413874574] [2, 2] 155713536  
380880.ex1 380880ex4 [0, 0, 0, -8409831987, -296844558897166] [2] 155713536  
380880.ex2 380880ex5 [0, 0, 0, -1967627667, 28776284585426] [2] 311427072  
380880.ex6 380880ex6 [0, 0, 0, 669585453, -21238805941486] [2] 311427072  

Rank

sage: E.rank()
 

The elliptic curves in class 380880ex have rank \(1\).

Modular form 380880.2.a.ex

sage: E.q_eigenform(10)
 
\( q + q^{5} - 4q^{11} - 2q^{13} - 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.