Properties

Label 17600.u
Number of curves $2$
Conductor $17600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 17600.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17600.u1 17600bb2 \([0, 1, 0, -353, -2177]\) \(595508/121\) \(991232000\) \([2]\) \(10240\) \(0.44189\)  
17600.u2 17600bb1 \([0, 1, 0, 47, -177]\) \(5488/11\) \(-22528000\) \([2]\) \(5120\) \(0.095312\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 17600.u have rank \(0\).

Complex multiplication

The elliptic curves in class 17600.u do not have complex multiplication.

Modular form 17600.2.a.u

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + 4 q^{7} + q^{9} - q^{11} + 6 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.