Properties

Label 2880bb
Number of curves 8
Conductor 2880
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("2880.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2880bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2880.q8 2880bb1 [0, 0, 0, 852, 29392] [2] 3072 \(\Gamma_0(N)\)-optimal
2880.q6 2880bb2 [0, 0, 0, -10668, 384208] [2, 2] 6144  
2880.q7 2880bb3 [0, 0, 0, -7788, -865712] [2] 9216  
2880.q5 2880bb4 [0, 0, 0, -39468, -2599472] [2] 12288  
2880.q4 2880bb5 [0, 0, 0, -166188, 26076112] [2] 12288  
2880.q3 2880bb6 [0, 0, 0, -192108, -32347568] [2, 2] 18432  
2880.q1 2880bb7 [0, 0, 0, -3072108, -2072539568] [2] 36864  
2880.q2 2880bb8 [0, 0, 0, -261228, -6994352] [2] 36864  

Rank

sage: E.rank()
 

The elliptic curves in class 2880bb have rank \(1\).

Modular form 2880.2.a.q

sage: E.q_eigenform(10)
 
\( q - q^{5} + 4q^{7} - 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.