Properties

Label 17600i
Number of curves $2$
Conductor $17600$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 17600i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17600.h2 17600i1 \([0, 1, 0, 2992, 21238]\) \(2961169856/1890625\) \(-1890625000000\) \([2]\) \(18432\) \(1.0446\) \(\Gamma_0(N)\)-optimal
17600.h1 17600i2 \([0, 1, 0, -12633, 161863]\) \(3484156096/1830125\) \(117128000000000\) \([2]\) \(36864\) \(1.3912\)  

Rank

sage: E.rank()
 

The elliptic curves in class 17600i have rank \(1\).

Complex multiplication

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

Modular form 17600.2.a.i

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