↑

Properties

Label 40898.bd
Number of curves $2$
Conductor $40898$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 40898.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40898.bd1 40898bx2 \([1, -1, 1, -4349247, 3831524337]\) \(-1064019559329/125497034\) \(-1073123453419356633866\) \([]\) \(3292800\) \(2.7712\)  
40898.bd2 40898bx1 \([1, -1, 1, -54957, -7570923]\) \(-2146689/1664\) \(-14228841667204736\) \([]\) \(470400\) \(1.7983\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 40898.bd have rank \(1\).

Complex multiplication

The elliptic curves in class 40898.bd do not have complex multiplication.

Modular form 40898.2.a.bd

sage: E.q_eigenform(10)
 
\(q + q^{2} - 3 q^{3} + q^{4} + q^{5} - 3 q^{6} + q^{7} + q^{8} + 6 q^{9} + q^{10} - 3 q^{12} + q^{14} - 3 q^{15} + q^{16} + 3 q^{17} + 6 q^{18} + 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.