Properties

Label 236992.cf
Number of curves $2$
Conductor $236992$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("cf1")
 
E.isogeny_class()
 

Elliptic curves in class 236992.cf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.cf1 236992cf2 \([0, -1, 0, -474689, -105620767]\) \(304821217/51842\) \(2011817982699241472\) \([2]\) \(4866048\) \(2.2328\)  
236992.cf2 236992cf1 \([0, -1, 0, -136129, 17818209]\) \(7189057/644\) \(24991527735394304\) \([2]\) \(2433024\) \(1.8862\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 236992.cf have rank \(0\).

Complex multiplication

The elliptic curves in class 236992.cf do not have complex multiplication.

Modular form 236992.2.a.cf

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} - 2 q^{5} + q^{7} + q^{9} - 6 q^{11} + 4 q^{13} - 4 q^{15} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.