Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2880.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2880.f1 2880ba3 \([0, 0, 0, -1488, -22088]\) \(488095744/125\) \(93312000\) \([2]\) \(1152\) \(0.51524\)  
2880.f2 2880ba4 \([0, 0, 0, -1308, -27632]\) \(-20720464/15625\) \(-186624000000\) \([2]\) \(2304\) \(0.86181\)  
2880.f3 2880ba1 \([0, 0, 0, -48, 88]\) \(16384/5\) \(3732480\) \([2]\) \(384\) \(-0.034070\) \(\Gamma_0(N)\)-optimal
2880.f4 2880ba2 \([0, 0, 0, 132, 592]\) \(21296/25\) \(-298598400\) \([2]\) \(768\) \(0.31250\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2880.2.a.f

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.