Properties

Label 2880.t
Number of curves 4
Conductor 2880
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("2880.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2880.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2880.t1 2880t3 [0, 0, 0, -3852, 92016] [2] 2048  
2880.t2 2880t2 [0, 0, 0, -252, 1296] [2, 2] 1024  
2880.t3 2880t1 [0, 0, 0, -72, -216] [2] 512 \(\Gamma_0(N)\)-optimal
2880.t4 2880t4 [0, 0, 0, 468, 7344] [2] 2048  

Rank

sage: E.rank()
 

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

Modular form 2880.2.a.t

sage: E.q_eigenform(10)
 
\( q + q^{5} - 4q^{7} + 4q^{11} + 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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 LMFDB 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 LMFDB labels.