Properties

Label 202800.bs
Number of curves $2$
Conductor $202800$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 202800.bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
202800.bs1 202800fe2 \([0, -1, 0, -3111008, 1893040512]\) \(10779215329/1232010\) \(380587325189760000000\) \([2]\) \(9289728\) \(2.6813\)  
202800.bs2 202800fe1 \([0, -1, 0, 268992, 148960512]\) \(6967871/35100\) \(-10842943737600000000\) \([2]\) \(4644864\) \(2.3347\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 202800.bs have rank \(2\).

Complex multiplication

The elliptic curves in class 202800.bs do not have complex multiplication.

Modular form 202800.2.a.bs

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{7} + q^{9} + 4q^{11} - 8q^{17} - 6q^{19} + O(q^{20})\)  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.