Properties

Label 2880d
Number of curves $2$
Conductor $2880$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 2880d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2880.g2 2880d1 \([0, 0, 0, 12, 32]\) \(1728/5\) \(-552960\) \([2]\) \(256\) \(-0.21464\) \(\Gamma_0(N)\)-optimal
2880.g1 2880d2 \([0, 0, 0, -108, 368]\) \(157464/25\) \(22118400\) \([2]\) \(512\) \(0.13194\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2880.2.a.d

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.