Properties

Label 2320.g
Number of curves $2$
Conductor $2320$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 2320.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2320.g1 2320h1 \([0, 0, 0, -32, 31]\) \(226492416/105125\) \(1682000\) \([2]\) \(288\) \(-0.11081\) \(\Gamma_0(N)\)-optimal
2320.g2 2320h2 \([0, 0, 0, 113, 234]\) \(623331504/453125\) \(-116000000\) \([2]\) \(576\) \(0.23576\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2320.g have rank \(1\).

Complex multiplication

The elliptic curves in class 2320.g do not have complex multiplication.

Modular form 2320.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{5} + 2 q^{7} - 3 q^{9} + 4 q^{11} - 6 q^{13} - 4 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.