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Properties

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

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Show commands: SageMath
Copy content sage:E = EllipticCurve("bc1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

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

Complex multiplication

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

Modular form 446160.2.a.bc

Copy content sage:E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{9} + q^{11} + q^{15} - 4 q^{17} - 2 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.

Elliptic curves in class 446160.bc

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
446160.bc1 446160bc2 \([0, -1, 0, -31548976, -68188658240]\) \(175654575624148921/21954418200\) \(434052232632417484800\) \([2]\) \(30965760\) \(2.9826\) \(\Gamma_0(N)\)-optimal*
446160.bc2 446160bc1 \([0, -1, 0, -1804976, -1252760640]\) \(-32894113444921/15289560000\) \(-302283922694307840000\) \([2]\) \(15482880\) \(2.6360\) \(\Gamma_0(N)\)-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 446160.bc1.