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Properties

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

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 84966w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
84966.i2 84966w1 \([1, 1, 0, -304756, -90948080]\) \(-1102302937/616896\) \(-1751837112579427776\) \([2]\) \(1327104\) \(2.2039\) \(\Gamma_0(N)\)-optimal
84966.i1 84966w2 \([1, 1, 0, -5402716, -4835109656]\) \(6141556990297/1019592\) \(2895397449957665352\) \([2]\) \(2654208\) \(2.5505\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 84966.2.a.w

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - 2 q^{5} + q^{6} - q^{8} + q^{9} + 2 q^{10} + 2 q^{11} - q^{12} - 4 q^{13} + 2 q^{15} + q^{16} - q^{18} + 2 q^{19} + O(q^{20})\) 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.