Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2880.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2880.e1 2880u2 \([0, 0, 0, -4428, -112752]\) \(3721734/25\) \(64497254400\) \([2]\) \(3072\) \(0.90887\)  
2880.e2 2880u1 \([0, 0, 0, -108, -3888]\) \(-108/5\) \(-6449725440\) \([2]\) \(1536\) \(0.56230\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2880.2.a.e

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.