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Properties

Label 481650.dw
Number of curves $2$
Conductor $481650$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("dw1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 481650.dw have rank \(1\).

Complex multiplication

The elliptic curves in class 481650.dw do not have complex multiplication.

Modular form 481650.2.a.dw

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} + 2 q^{7} - q^{8} + q^{9} + 3 q^{11} + q^{12} - 2 q^{14} + q^{16} - 2 q^{17} - q^{18} + q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 481650.dw

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
481650.dw1 481650dw2 \([1, 0, 1, -83974076, -296243229202]\) \(-1389310279182025/267418692\) \(-12605263176892851562500\) \([]\) \(69120000\) \(3.2411\)  
481650.dw2 481650dw1 \([1, 0, 1, 806464, 16664078]\) \(480705753733655/279172334592\) \(-33687788428991923200\) \([]\) \(13824000\) \(2.4364\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 481650.dw1.