Cremona's table of elliptic curves

238 = 2 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2- 7- 17-	Signs for the Atkin-Lehner involutions
Class	238c	Isogeny class
Conductor	238	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	8185058 = 2 · 72 · 174	Discriminant
Eigenvalues	2-  0  2 7-  0 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-529,-4545]	[a1,a2,a3,a4,a6]
j	16342588257633/8185058	j-invariant
L	1.9913282031166	L(r)(E,1)/r!
Ω	0.99566410155831	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1904c3 7616e3 2142h3 5950a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 238c3

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	0	2	-	0	-2	-	4	0	-6	0	-6	-6	-12	8	-2	4	2	12	0	2	-8	12	10	-14

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Quadratic twists for elliptic curve 238c3

-4	8	-3	5	-7	-11	13	17	-19	-23
1904c3	7616e3	2142h3	5950a3	1666k3	28798b4	40222e4	4046i3	85918u4	125902l4

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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