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	1938g	Isogeny class
Conductor	1938	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	144105804 = 22 · 38 · 172 · 19	Discriminant
Eigenvalues	2- 3+ -2  2 -6  2 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-434,3251]	[a1,a2,a3,a4,a6]
Generators	[17:25:1]	Generators of the group modulo torsion
j	9041811349537/144105804	j-invariant
L	3.4568237698343	L(r)(E,1)/r!
Ω	1.8387713738594	Real period
R	0.93998194092472	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	15504u2 62016v2 5814i2 48450q2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1938g2

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

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Quadratic twists for elliptic curve 1938g2

-4	8	-3	5	-7	17	-19
15504u2	62016v2	5814i2	48450q2	94962cd2	32946w2	36822l2

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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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