Properties

Label 223080.cb
Number of curves $4$
Conductor $223080$
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 223080.cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
223080.cb1 223080be3 \([0, -1, 0, -4336684720, 109923513052300]\) \(912446049969377120252018/17177299425\) \(169802841006663321600\) \([2]\) \(115605504\) \(3.8698\)  
223080.cb2 223080be4 \([0, -1, 0, -295218720, 1393057075500]\) \(287849398425814280018/81784533026485575\) \(808465039509581438525798400\) \([2]\) \(115605504\) \(3.8698\)  
223080.cb3 223080be2 \([0, -1, 0, -271051720, 1717503883900]\) \(445574312599094932036/61129333175625\) \(302141046308971858560000\) \([2, 2]\) \(57802752\) \(3.5232\)  
223080.cb4 223080be1 \([0, -1, 0, -15439220, 31790568900]\) \(-329381898333928144/162600887109375\) \(-200919916878723900000000\) \([4]\) \(28901376\) \(3.1767\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 223080.cb have rank \(0\).

Complex multiplication

The elliptic curves in class 223080.cb do not have complex multiplication.

Modular form 223080.2.a.cb

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.