Cremona's table of elliptic curves

1938 = 2 · 3 · 17 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3- 17- 19+	Signs for the Atkin-Lehner involutions
Class	1938f	Isogeny class
Conductor	1938	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-257077638 = -1 · 2 · 34 · 174 · 19	Discriminant
Eigenvalues	2+ 3- -2  0  4 -6 17- 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,148,344]	[a1,a2,a3,a4,a6]
Generators	[2:24:1]	Generators of the group modulo torsion
j	362009757383/257077638	j-invariant
L	2.4065729334887	L(r)(E,1)/r!
Ω	1.1092376424098	Real period
R	0.54239345147457	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	15504r4 62016q3 5814p4 48450w3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1938f4

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

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Quadratic twists for elliptic curve 1938f4

-4	8	-3	5	-7	17	-19
15504r4	62016q3	5814p4	48450w3	94962i3	32946b3	36822u3

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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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