Properties

Label 288990.go
Number of curves $2$
Conductor $288990$
CM no
Rank $0$
Graph

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

Elliptic curves in class 288990.go

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
288990.go1 288990go2 \([1, -1, 1, -45662, 3707799]\) \(2992209121/54150\) \(190539974658150\) \([2]\) \(1474560\) \(1.5354\)  
288990.go2 288990go1 \([1, -1, 1, -32, 166911]\) \(-1/3420\) \(-12034103662620\) \([2]\) \(737280\) \(1.1888\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 288990.go have rank \(0\).

Complex multiplication

The elliptic curves in class 288990.go do not have complex multiplication.

Modular form 288990.2.a.go

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + 2 q^{7} + q^{8} + q^{10} + 2 q^{14} + q^{16} - 8 q^{17} - q^{19} + O(q^{20})\) 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.