Properties

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

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

Elliptic curves in class 2880.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2880.t1 2880t3 \([0, 0, 0, -3852, 92016]\) \(132304644/5\) \(238878720\) \([2]\) \(2048\) \(0.69367\)  
2880.t2 2880t2 \([0, 0, 0, -252, 1296]\) \(148176/25\) \(298598400\) \([2, 2]\) \(1024\) \(0.34709\)  
2880.t3 2880t1 \([0, 0, 0, -72, -216]\) \(55296/5\) \(3732480\) \([2]\) \(512\) \(0.00051877\) \(\Gamma_0(N)\)-optimal
2880.t4 2880t4 \([0, 0, 0, 468, 7344]\) \(237276/625\) \(-29859840000\) \([2]\) \(2048\) \(0.69367\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 2880.t do not have complex multiplication.

Modular form 2880.2.a.t

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

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.