↑

Properties

Label 170093d
Number of curves $2$
Conductor $170093$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 170093d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
170093.d2 170093d1 \([1, 1, 0, 7686, -980833]\) \(4657463/41503\) \(-447369773799487\) \([2]\) \(608304\) \(1.4925\) \(\Gamma_0(N)\)-optimal
170093.d1 170093d2 \([1, 1, 0, -113809, -13689210]\) \(15124197817/1294139\) \(13949802946656731\) \([2]\) \(1216608\) \(1.8391\)  

Rank

sage: E.rank()
 

The elliptic curves in class 170093d have rank \(0\).

Complex multiplication

The elliptic curves in class 170093d do not have complex multiplication.

Modular form 170093.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{2} + 2 q^{3} - q^{4} + 2 q^{5} + 2 q^{6} - q^{7} - 3 q^{8} + q^{9} + 2 q^{10} - q^{11} - 2 q^{12} - 4 q^{13} - q^{14} + 4 q^{15} - q^{16} + 4 q^{17} + q^{18} + O(q^{20})\) 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.