↑

Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 2320a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2320.h2 2320a1 \([0, -1, 0, -11, -10]\) \(10061824/725\) \(11600\) \([2]\) \(128\) \(-0.47343\) \(\Gamma_0(N)\)-optimal
2320.h1 2320a2 \([0, -1, 0, -36, 80]\) \(20720464/4205\) \(1076480\) \([2]\) \(256\) \(-0.12685\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2320.2.a.a

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} - q^{5} + q^{9} - 4 q^{11} - 2 q^{13} - 2 q^{15} - 4 q^{19} + O(q^{20})\) 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.