Properties

Label 193600bd
Number of curves $2$
Conductor $193600$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 193600bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
193600.bz2 193600bd1 [0, 1, 0, -48033, 4036063] [] 430080 \(\Gamma_0(N)\)-optimal
193600.bz1 193600bd2 [0, 1, 0, -488033, -513139937] [] 4730880  

Rank

sage: E.rank()
 

The elliptic curves in class 193600bd have rank \(1\).

Complex multiplication

The elliptic curves in class 193600bd do not have complex multiplication.

Modular form 193600.2.a.bd

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

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.