Properties

Label 236691.w
Number of curves $2$
Conductor $236691$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 236691.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236691.w1 236691w1 \([1, -1, 0, -13527855, 19151906168]\) \(420100556152674123/62939003491\) \(41018252567991841233\) \([2]\) \(13271040\) \(2.7766\) \(\Gamma_0(N)\)-optimal
236691.w2 236691w2 \([1, -1, 0, -12275040, 22841446343]\) \(-313859434290315003/164114213839849\) \(-106955590331882975051187\) \([2]\) \(26542080\) \(3.1232\)  

Rank

sage: E.rank()
 

The elliptic curves in class 236691.w have rank \(0\).

Complex multiplication

The elliptic curves in class 236691.w do not have complex multiplication.

Modular form 236691.2.a.w

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