↑

Properties

Label 333795.cb
Number of curves $2$
Conductor $333795$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 333795.cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333795.cb1 333795cb1 \([1, 0, 1, -2297123, -1314935719]\) \(55537031513298889/1202869847025\) \(29034353930585382225\) \([2]\) \(10063872\) \(2.5231\) \(\Gamma_0(N)\)-optimal
333795.cb2 333795cb2 \([1, 0, 1, 181052, -4003259959]\) \(27192154047911/286843427678115\) \(-6923703027777010602435\) \([2]\) \(20127744\) \(2.8697\)  

Rank

sage: E.rank()
 

The elliptic curves in class 333795.cb have rank \(0\).

Complex multiplication

The elliptic curves in class 333795.cb do not have complex multiplication.

Modular form 333795.2.a.cb

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} + q^{7} - 3 q^{8} + q^{9} + q^{10} - q^{11} - q^{12} - 2 q^{13} + q^{14} + q^{15} - q^{16} + q^{18} - 2 q^{19} + O(q^{20})\) 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.