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Properties

Label 2880k
Number of curves $2$
Conductor $2880$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 2880k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2880.d2 2880k1 \([0, 0, 0, -3, -52]\) \(-64/25\) \(-1166400\) \([2]\) \(384\) \(-0.15674\) \(\Gamma_0(N)\)-optimal
2880.d1 2880k2 \([0, 0, 0, -228, -1312]\) \(438976/5\) \(14929920\) \([2]\) \(768\) \(0.18983\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2880.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{5} - 2 q^{7} - 4 q^{11} + 6 q^{13} - 2 q^{17} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.