Properties

Label 5880bf
Number of curves $6$
Conductor $5880$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("5880.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5880bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5880.t4 5880bf1 [0, 1, 0, -8591, -309366] [2] 6144 \(\Gamma_0(N)\)-optimal
5880.t3 5880bf2 [0, 1, 0, -8836, -291040] [2, 2] 12288  
5880.t2 5880bf3 [0, 1, 0, -33336, 2021760] [2, 2] 24576  
5880.t5 5880bf4 [0, 1, 0, 11744, -1427056] [2] 24576  
5880.t1 5880bf5 [0, 1, 0, -513536, 141471840] [2] 49152  
5880.t6 5880bf6 [0, 1, 0, 54864, 10982880] [2] 49152  

Rank

sage: E.rank()
 

The elliptic curves in class 5880bf have rank \(0\).

Modular form 5880.2.a.t

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{5} + q^{9} - 4q^{11} + 2q^{13} - q^{15} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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.