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Properties

Label 143550.fw
Number of curves $4$
Conductor $143550$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("fw1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 143550.fw have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1\)
\(5\)\(1\)
\(11\)\(1 - T\)
\(29\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 - 4 T + 7 T^{2}\) 1.7.ae
\(13\) \( 1 - 4 T + 13 T^{2}\) 1.13.ae
\(17\) \( 1 + 6 T + 17 T^{2}\) 1.17.g
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 23 T^{2}\) 1.23.a
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 143550.fw do not have complex multiplication.

Modular form 143550.2.a.fw

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 4 q^{7} + q^{8} + q^{11} + 4 q^{13} + 4 q^{14} + q^{16} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 143550.fw

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
143550.fw1 143550bx4 \([1, -1, 1, -58702055, 173122234197]\) \(1963975500122834382625/62995224591882\) \(717554980116905906250\) \([2]\) \(17915904\) \(3.0968\)  
143550.fw2 143550bx3 \([1, -1, 1, -3826805, 2460206697]\) \(544107922591866625/85504662747108\) \(973951549103777062500\) \([2]\) \(8957952\) \(2.7502\)  
143550.fw3 143550bx2 \([1, -1, 1, -1293305, -183300303]\) \(21002873311842625/10875667967208\) \(123880655438978625000\) \([2]\) \(5971968\) \(2.5475\)  
143550.fw4 143550bx1 \([1, -1, 1, -1032305, -403062303]\) \(10680703423890625/11653595712\) \(132741738657000000\) \([2]\) \(2985984\) \(2.2009\) \(\Gamma_0(N)\)-optimal