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	1938h	Isogeny class
Conductor	1938	Conductor
∏ cp	168	Product of Tamagawa factors cp
Δ	-9735147648 = -1 · 27 · 36 · 172 · 192	Discriminant
Eigenvalues	2- 3- -2 -2 -4  0 17+ 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,501,-1935]	[a1,a2,a3,a4,a6]
Generators	[42:-327:1]	Generators of the group modulo torsion
j	13905375151823/9735147648	j-invariant
L	4.2558606826783	L(r)(E,1)/r!
Ω	0.72924805762791	Real period
R	0.13895136941996	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	15504o2 62016i2 5814f2 48450d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1938h2

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

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Quadratic twists for elliptic curve 1938h2

-4	8	-3	5	-7	17	-19
15504o2	62016i2	5814f2	48450d2	94962bs2	32946p2	36822c2

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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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