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Properties

Label 436800nq
Number of curves $2$
Conductor $436800$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("nq1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 436800nq have rank \(1\).

Complex multiplication

The elliptic curves in class 436800nq do not have complex multiplication.

Modular form 436800.2.a.nq

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

Isogeny matrix

Copy content 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

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.

Elliptic curves in class 436800nq

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
436800.nq1 436800nq1 \([0, 1, 0, -20333, -1115037]\) \(58107136000/464373\) \(7429968000000\) \([2]\) \(884736\) \(1.2973\) \(\Gamma_0(N)\)-optimal
436800.nq2 436800nq2 \([0, 1, 0, -6833, -2559537]\) \(-137842000/10955763\) \(-2804675328000000\) \([2]\) \(1769472\) \(1.6438\)