Properties

Label 17850.bt
Number of curves $2$
Conductor $17850$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("bt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17850.bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17850.bt1 17850bp2 \([1, 0, 0, -12963, 417417]\) \(15417797707369/4080067320\) \(63751051875000\) \([2]\) \(55296\) \(1.3574\)  
17850.bt2 17850bp1 \([1, 0, 0, 2037, 42417]\) \(59822347031/83966400\) \(-1311975000000\) \([2]\) \(27648\) \(1.0108\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 17850.bt have rank \(1\).

Complex multiplication

The elliptic curves in class 17850.bt do not have complex multiplication.

Modular form 17850.2.a.bt

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - q^{7} + q^{8} + q^{9} + 2q^{11} + q^{12} + 2q^{13} - q^{14} + q^{16} - q^{17} + q^{18} - 4q^{19} + O(q^{20})\)  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.