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Properties

Label 446160w
Number of curves $2$
Conductor $446160$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("w1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 446160w have rank \(1\).

Complex multiplication

The elliptic curves in class 446160w do not have complex multiplication.

Modular form 446160.2.a.w

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} - q^{11} + q^{15} + 2 q^{19} + O(q^{20})\) 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 446160w

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
446160.w2 446160w1 \([0, -1, 0, -3096136, 2102957440]\) \(-664085303622724/1843359375\) \(-9111084668400000000\) \([2]\) \(9633792\) \(2.5109\) \(\Gamma_0(N)\)-optimal*
446160.w1 446160w2 \([0, -1, 0, -49571136, 134352217440]\) \(1362762798430761362/10456875\) \(103369396965120000\) \([2]\) \(19267584\) \(2.8574\) \(\Gamma_0(N)\)-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 446160w1.