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	3755844 = 22 · 32 · 172 · 192	Discriminant
Eigenvalues	2+ 3- -2  0  4 -6 17- 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-42,40]	[a1,a2,a3,a4,a6]
Generators	[-1:9:1]	Generators of the group modulo torsion
j	7916293657/3755844	j-invariant
L	2.4065729334887	L(r)(E,1)/r!
Ω	2.2184752848196	Real period
R	1.0847869029491	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	15504r2 62016q2 5814p2 48450w2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1938f2

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 1938f2

-4	8	-3	5	-7	17	-19
15504r2	62016q2	5814p2	48450w2	94962i2	32946b2	36822u2

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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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