Properties

Label 2640o
Number of curves $4$
Conductor $2640$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 2640o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2640.b4 2640o1 \([0, -1, 0, 219, 4500]\) \(72268906496/606436875\) \(-9702990000\) \([2]\) \(1152\) \(0.59767\) \(\Gamma_0(N)\)-optimal
2640.b3 2640o2 \([0, -1, 0, -3156, 63900]\) \(13584145739344/1195803675\) \(306125740800\) \([2]\) \(2304\) \(0.94425\)  
2640.b2 2640o3 \([0, -1, 0, -15621, 757296]\) \(-26348629355659264/24169921875\) \(-386718750000\) \([2]\) \(3456\) \(1.1470\)  
2640.b1 2640o4 \([0, -1, 0, -249996, 48194796]\) \(6749703004355978704/5671875\) \(1452000000\) \([2]\) \(6912\) \(1.4936\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2640o have rank \(0\).

Complex multiplication

The elliptic curves in class 2640o do not have complex multiplication.

Modular form 2640.2.a.o

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