↑

Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("ds1")
 
E.isogeny_class()
 

Elliptic curves in class 84966.ds

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
84966.ds1 84966dm2 \([1, 0, 0, -1996996, -1127118448]\) \(-6329617441/279936\) \(-38952613444413158784\) \([]\) \(2897664\) \(2.5240\)  
84966.ds2 84966dm1 \([1, 0, 0, -14456, 1541574]\) \(-2401/6\) \(-834889691452614\) \([]\) \(413952\) \(1.5511\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 84966.2.a.ds

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 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.