Properties

Label 2736.o
Number of curves $4$
Conductor $2736$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 2736.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2736.o1 2736n3 \([0, 0, 0, -61635, -5889598]\) \(8671983378625/82308\) \(245770371072\) \([2]\) \(6912\) \(1.3480\)  
2736.o2 2736n4 \([0, 0, 0, -60195, -6177886]\) \(-8078253774625/846825858\) \(-2528608462774272\) \([2]\) \(13824\) \(1.6945\)  
2736.o3 2736n1 \([0, 0, 0, -1155, 1154]\) \(57066625/32832\) \(98035826688\) \([2]\) \(2304\) \(0.79865\) \(\Gamma_0(N)\)-optimal
2736.o4 2736n2 \([0, 0, 0, 4605, 9218]\) \(3616805375/2105352\) \(-6286547386368\) \([2]\) \(4608\) \(1.1452\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2736.o have rank \(1\).

Complex multiplication

The elliptic curves in class 2736.o do not have complex multiplication.

Modular form 2736.2.a.o

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.