Properties

Label 289800.bw
Number of curves $2$
Conductor $289800$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("bw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 289800.bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
289800.bw1 289800bw1 \([0, 0, 0, -19575, 290250]\) \(10536048/5635\) \(443654820000000\) \([2]\) \(1105920\) \(1.5018\) \(\Gamma_0(N)\)-optimal
289800.bw2 289800bw2 \([0, 0, 0, 74925, 2274750]\) \(147704148/92575\) \(-29154459600000000\) \([2]\) \(2211840\) \(1.8483\)  

Rank

sage: E.rank()
 

The elliptic curves in class 289800.bw have rank \(0\).

Complex multiplication

The elliptic curves in class 289800.bw do not have complex multiplication.

Modular form 289800.2.a.bw

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