Properties

Label 450800n
Number of curves $2$
Conductor $450800$
CM no
Rank $1$
Graph

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

Elliptic curves in class 450800n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
450800.n2 450800n1 \([0, 1, 0, -34708, 3186588]\) \(-9826000/3703\) \(-1742616988000000\) \([2]\) \(2211840\) \(1.6343\) \(\Gamma_0(N)\)-optimal*
450800.n1 450800n2 \([0, 1, 0, -598208, 177871588]\) \(12576878500/1127\) \(2121446768000000\) \([2]\) \(4423680\) \(1.9809\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 450800n1.

Rank

sage: E.rank()
 

The elliptic curves in class 450800n have rank \(1\).

Complex multiplication

The elliptic curves in class 450800n do not have complex multiplication.

Modular form 450800.2.a.n

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