Properties

Label 2496.o
Number of curves $2$
Conductor $2496$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2496.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2496.o1 2496v2 \([0, -1, 0, -81, 273]\) \(3631696/507\) \(8306688\) \([2]\) \(768\) \(0.054047\)  
2496.o2 2496v1 \([0, -1, 0, -21, -27]\) \(1048576/117\) \(119808\) \([2]\) \(384\) \(-0.29253\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2496.o have rank \(0\).

Complex multiplication

The elliptic curves in class 2496.o do not have complex multiplication.

Modular form 2496.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{3} + 4q^{5} + 2q^{7} + q^{9} - 4q^{11} - q^{13} - 4q^{15} + 2q^{17} - 2q^{19} + O(q^{20})\)  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.