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Properties

Label 163170ft
Number of curves $2$
Conductor $163170$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ft1")
 
E.isogeny_class()
 

Elliptic curves in class 163170ft

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
163170.h2 163170ft1 \([1, -1, 0, -870, 4696]\) \(55081072683/25326500\) \(33506959500\) \([]\) \(152064\) \(0.71437\) \(\Gamma_0(N)\)-optimal
163170.h1 163170ft2 \([1, -1, 0, -59145, 5551181]\) \(23724363979827/11840\) \(11419289280\) \([]\) \(456192\) \(1.2637\)  

Rank

sage: E.rank()
 

The elliptic curves in class 163170ft have rank \(1\).

Complex multiplication

The elliptic curves in class 163170ft do not have complex multiplication.

Modular form 163170.2.a.ft

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.