Properties

Label 2880.r
Number of curves $4$
Conductor $2880$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2880.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2880.r1 2880l4 \([0, 0, 0, -7788, 264368]\) \(546718898/405\) \(38698352640\) \([2]\) \(4096\) \(0.96528\)  
2880.r2 2880l3 \([0, 0, 0, -4908, -130768]\) \(136835858/1875\) \(179159040000\) \([2]\) \(4096\) \(0.96528\)  
2880.r3 2880l2 \([0, 0, 0, -588, 2288]\) \(470596/225\) \(10749542400\) \([2, 2]\) \(2048\) \(0.61871\)  
2880.r4 2880l1 \([0, 0, 0, 132, 272]\) \(21296/15\) \(-179159040\) \([2]\) \(1024\) \(0.27214\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2880.r have rank \(0\).

Complex multiplication

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

Modular form 2880.2.a.r

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.