↑

Properties

Label 187850.w
Number of curves $2$
Conductor $187850$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 187850.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187850.w1 187850bq1 \([1, 1, 0, -6076375, -5766952875]\) \(65787589563409/10400000\) \(3922354962500000000\) \([2]\) \(9830400\) \(2.5783\) \(\Gamma_0(N)\)-optimal
187850.w2 187850bq2 \([1, 1, 0, -5498375, -6907346875]\) \(-48743122863889/26406250000\) \(-9959104396972656250000\) \([2]\) \(19660800\) \(2.9249\)  

Rank

sage: E.rank()
 

The elliptic curves in class 187850.w have rank \(0\).

Complex multiplication

The elliptic curves in class 187850.w do not have complex multiplication.

Modular form 187850.2.a.w

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