Properties

Label 84966u
Number of curves $2$
Conductor $84966$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 84966u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
84966.bb2 84966u1 \([1, 1, 0, -47220149, -140442814035]\) \(-4100379159705193/626805817344\) \(-1779978623955903703793664\) \([2]\) \(18579456\) \(3.3824\) \(\Gamma_0(N)\)-optimal
84966.bb1 84966u2 \([1, 1, 0, -781326389, -8406332255187]\) \(18575453384550358633/352517816448\) \(1001066295938163049461888\) \([2]\) \(37158912\) \(3.7290\)  

Rank

sage: E.rank()
 

The elliptic curves in class 84966u have rank \(0\).

Complex multiplication

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

Modular form 84966.2.a.u

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.