Properties

Label 132600.n
Number of curves $2$
Conductor $132600$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 132600.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
132600.n1 132600ci1 \([0, -1, 0, -7025408, 7158898812]\) \(2396726313900986596/4154072495625\) \(66465159930000000000\) \([2]\) \(4423680\) \(2.6975\) \(\Gamma_0(N)\)-optimal
132600.n2 132600ci2 \([0, -1, 0, -4828408, 11715476812]\) \(-389032340685029858/1627263833203125\) \(-52072442662500000000000\) \([2]\) \(8847360\) \(3.0441\)  

Rank

sage: E.rank()
 

The elliptic curves in class 132600.n have rank \(1\).

Complex multiplication

The elliptic curves in class 132600.n do not have complex multiplication.

Modular form 132600.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} + 2 q^{11} + q^{13} + q^{17} - 8 q^{19} + O(q^{20})\) 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.