↑

Properties

Label 21294.bx
Number of curves $2$
Conductor $21294$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bx1")
 
E.isogeny_class()
 

Elliptic curves in class 21294.bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21294.bx1 21294cd2 \([1, -1, 1, -5588908448, 160820859920933]\) \(-5486773802537974663600129/2635437714\) \(-9273430013641602354\) \([]\) \(11063808\) \(3.8783\)  
21294.bx2 21294cd1 \([1, -1, 1, 1085962, 4921277573]\) \(40251338884511/2997011332224\) \(-10545714926909498254464\) \([]\) \(1580544\) \(2.9054\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 21294.bx have rank \(1\).

Complex multiplication

The elliptic curves in class 21294.bx do not have complex multiplication.

Modular form 21294.2.a.bx

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - q^{10} + 5 q^{11} - q^{14} + q^{16} + 3 q^{17} + q^{19} + O(q^{20})\) 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.