Properties

Label 115920.cb
Number of curves $6$
Conductor $115920$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("cb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.cb1 115920dm6 \([0, 0, 0, -12195363, -16392292702]\) \(67176973097223766561/91487391870\) \(273179888325550080\) \([2]\) \(3145728\) \(2.6199\)  
115920.cb2 115920dm4 \([0, 0, 0, -768963, -251360062]\) \(16840406336564161/604708416900\) \(1805649657528729600\) \([2, 2]\) \(1572864\) \(2.2733\)  
115920.cb3 115920dm2 \([0, 0, 0, -120963, 10820738]\) \(65553197996161/20996010000\) \(62693749923840000\) \([2, 2]\) \(786432\) \(1.9267\)  
115920.cb4 115920dm1 \([0, 0, 0, -109443, 13933442]\) \(48551226272641/9273600\) \(27690821222400\) \([2]\) \(393216\) \(1.5802\) \(\Gamma_0(N)\)-optimal
115920.cb5 115920dm5 \([0, 0, 0, 289437, -889998622]\) \(898045580910239/115117148363070\) \(-343737963137753210880\) \([2]\) \(3145728\) \(2.6199\)  
115920.cb6 115920dm3 \([0, 0, 0, 342717, 73788482]\) \(1490881681033919/1650501562500\) \(-4928371257600000000\) \([2]\) \(1572864\) \(2.2733\)  

Rank

sage: E.rank()
 

The elliptic curves in class 115920.cb have rank \(0\).

Complex multiplication

The elliptic curves in class 115920.cb do not have complex multiplication.

Modular form 115920.2.a.cb

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 1 & 8 & 4 \\ 4 & 2 & 4 & 8 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.