Properties

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

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 2880o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2880.c3 2880o1 \([0, 0, 0, -8103, -280748]\) \(1261112198464/675\) \(31492800\) \([2]\) \(3072\) \(0.76837\) \(\Gamma_0(N)\)-optimal
2880.c2 2880o2 \([0, 0, 0, -8148, -277472]\) \(20034997696/455625\) \(1360488960000\) \([2, 2]\) \(6144\) \(1.1149\)  
2880.c1 2880o3 \([0, 0, 0, -17868, 511792]\) \(26410345352/10546875\) \(251942400000000\) \([2]\) \(12288\) \(1.4615\)  
2880.c4 2880o4 \([0, 0, 0, 852, -857072]\) \(2863288/13286025\) \(-317374864588800\) \([2]\) \(12288\) \(1.4615\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2880.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{5} - 4 q^{7} + 4 q^{11} - 6 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.