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	238a	Isogeny class
Conductor	238	Conductor
∏ cp	56	Product of Tamagawa factors cp
Δ	88817792 = 27 · 74 · 172	Discriminant
Eigenvalues	2- -2 -4 7- -6 -2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-700,7056]	[a1,a2,a3,a4,a6]
Generators	[-14:126:1]	Generators of the group modulo torsion
j	37936442980801/88817792	j-invariant
L	1.4310007528473	L(r)(E,1)/r!
Ω	1.9151889278601	Real period
R	0.053370368845699	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1904a2 7616c2 2142k2 5950b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 238a2

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
-	-2	-4	-	-6	-2	+	0	-4	8	0	4	-2	-8	-8	-6	-4	-8	-16	4	10	-12	12	10	6

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Quadratic twists for elliptic curve 238a2

-4	8	-3	5	-7	-11	13	17	-19	-23
1904a2	7616c2	2142k2	5950b2	1666m2	28798e2	40222d2	4046l2	85918k2	125902p2

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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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