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
deg	16	Modular degree for the optimal curve
Δ	13328 = 24 · 72 · 17	Discriminant
Eigenvalues	2-  0  2 7-  0 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-19,35]	[a1,a2,a3,a4,a6]
j	721734273/13328	j-invariant
L	1.9913282031166	L(r)(E,1)/r!
Ω	3.9826564062332	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1904c1 7616e1 2142h1 5950a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 238c1

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 238c1

-4	8	-3	5	-7	-11	13	17	-19	-23
1904c1	7616e1	2142h1	5950a1	1666k1	28798b1	40222e1	4046i1	85918u1	125902l1

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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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