↑

Properties

Label 84966ct
Number of curves $2$
Conductor $84966$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("ct1")
 
E.isogeny_class()
 

Elliptic curves in class 84966ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
84966.cx2 84966ct1 \([1, 1, 1, -295, -4621]\) \(-2401/6\) \(-7096445286\) \([]\) \(59136\) \(0.57813\) \(\Gamma_0(N)\)-optimal
84966.cx1 84966ct2 \([1, 1, 1, -40755, 3268593]\) \(-6329617441/279936\) \(-331091751263616\) \([]\) \(413952\) \(1.5511\)  

Rank

sage: E.rank()
 

The elliptic curves in class 84966ct have rank \(1\).

Complex multiplication

The elliptic curves in class 84966ct do not have complex multiplication.

Modular form 84966.2.a.ct

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} - 5 q^{11} - q^{12} - q^{15} + q^{16} + q^{18} - 8 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.