Properties

Label 170352.go
Number of curves $2$
Conductor $170352$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("go1")
 
E.isogeny_class()
 

Elliptic curves in class 170352.go

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
170352.go1 170352gn1 \([0, 0, 0, -14703, 681070]\) \(10536048/91\) \(3036024246528\) \([2]\) \(602112\) \(1.2195\) \(\Gamma_0(N)\)-optimal
170352.go2 170352gn2 \([0, 0, 0, -4563, 1603810]\) \(-78732/8281\) \(-1105112825736192\) \([2]\) \(1204224\) \(1.5661\)  

Rank

sage: E.rank()
 

The elliptic curves in class 170352.go have rank \(0\).

Complex multiplication

The elliptic curves in class 170352.go do not have complex multiplication.

Modular form 170352.2.a.go

sage: E.q_eigenform(10)
 
\(q + 4 q^{5} + q^{7} + 4 q^{11} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.