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Properties

Label 450800df
Number of curves $2$
Conductor $450800$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("df1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 450800df have rank \(0\).

Complex multiplication

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

Modular form 450800.2.a.df

Copy content sage:E.q_eigenform(10)
 
\(q - 3 q^{9} - 2 q^{11} + 4 q^{13} - 6 q^{17} - 8 q^{19} + O(q^{20})\) 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 450800df

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
450800.df1 450800df1 \([0, 0, 0, -3188675, -2190826750]\) \(476196576129/197225\) \(1485012737600000000\) \([2]\) \(10616832\) \(2.4488\) \(\Gamma_0(N)\)-optimal
450800.df2 450800df2 \([0, 0, 0, -2698675, -2887116750]\) \(-288673724529/311181605\) \(-2343053097385280000000\) \([2]\) \(21233664\) \(2.7954\)