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	16	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	7953552 = 24 · 34 · 17 · 192	Discriminant
Eigenvalues	2- 3+ -2  2 -6  2 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-54,-93]	[a1,a2,a3,a4,a6]
Generators	[-5:11:1]	Generators of the group modulo torsion
j	17434421857/7953552	j-invariant
L	3.4568237698343	L(r)(E,1)/r!
Ω	1.8387713738594	Real period
R	0.46999097046236	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	15504u1 62016v1 5814i1 48450q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1938g1

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 1938g1

-4	8	-3	5	-7	17	-19
15504u1	62016v1	5814i1	48450q1	94962cd1	32946w1	36822l1

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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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