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	238b	Isogeny class
Conductor	238	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	28322 = 2 · 72 · 172	Discriminant
Eigenvalues	2+  0 -2 7+ -2  0 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-8,6]	[a1,a2,a3,a4,a6]
Generators	[-1:4:1]	Generators of the group modulo torsion
j	60698457/28322	j-invariant
L	1.072323770296	L(r)(E,1)/r!
Ω	3.340744690228	Real period
R	0.32098345420787	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	1904d2 7616a2 2142p2 5950p2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 238b2

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	+	-2	0	+	-2	-8	0	8	-4	-6	4	8	-6	10	10	8	4	-10	-4	-6	-6	-14

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Quadratic twists for elliptic curve 238b2

-4	8	-3	5	-7	-11	13	17	-19	-23
1904d2	7616a2	2142p2	5950p2	1666d2	28798ba2	40222u2	4046e2	85918bc2	125902g2

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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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