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Properties

Label 262080jw
Number of curves $8$
Conductor $262080$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("jw1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 262080jw have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(5\)\(1 - T\)
\(7\)\(1 + T\)
\(13\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 - 4 T + 11 T^{2}\) 1.11.ae
\(17\) \( 1 + 2 T + 17 T^{2}\) 1.17.c
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 2 T + 29 T^{2}\) 1.29.c
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 262080jw do not have complex multiplication.

Modular form 262080.2.a.jw

Copy content sage:E.q_eigenform(10)
 
\(q + q^{5} - q^{7} + 4 q^{11} - q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 2 & 2 \\ 8 & 4 & 2 & 8 & 4 & 1 & 8 & 8 \\ 16 & 8 & 4 & 16 & 2 & 8 & 1 & 4 \\ 16 & 8 & 4 & 16 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 262080jw

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
262080.jw7 262080jw1 \([0, 0, 0, -12533772, -17305600016]\) \(-1139466686381936641/17587891077120\) \(-3361098326401477509120\) \([2]\) \(12582912\) \(2.9327\) \(\Gamma_0(N)\)-optimal
262080.jw5 262080jw2 \([0, 0, 0, -201277452, -1099108876304]\) \(4718909406724749250561/1098974822400\) \(210017359109711462400\) \([2, 2]\) \(25165824\) \(3.2793\)  
262080.jw4 262080jw3 \([0, 0, 0, -202014732, -1090651095056]\) \(4770955732122964500481/71987251059360000\) \(13756977911502848655360000\) \([2, 2]\) \(50331648\) \(3.6259\)  
262080.jw2 262080jw4 \([0, 0, 0, -3220439052, -70342976339984]\) \(19328649688935739391016961/1048320\) \(200337071800320\) \([2]\) \(50331648\) \(3.6259\)  
262080.jw3 262080jw5 \([0, 0, 0, -396702732, 1352060303344]\) \(36128658497509929012481/16775330746084419600\) \(3205815628961032932792729600\) \([2, 2]\) \(100663296\) \(3.9725\)  
262080.jw6 262080jw6 \([0, 0, 0, -19123212, -2992064493584]\) \(-4047051964543660801/20235220197806250000\) \(-3867010799816083046400000000\) \([2]\) \(100663296\) \(3.9725\)  
262080.jw1 262080jw7 \([0, 0, 0, -5309579532, 148830726387184]\) \(86623684689189325642735681/56690726941459561860\) \(10833766630116300055102095360\) \([2]\) \(201326592\) \(4.3190\)  
262080.jw8 262080jw8 \([0, 0, 0, 1401166068, 10206923717104]\) \(1591934139020114746758719/1156766383092650262660\) \(-221061498345761548921507676160\) \([2]\) \(201326592\) \(4.3190\)