Cremona's table of elliptic curves

38 = 2 · 19

Field	Data	Notes
Atkin-Lehner	2+ 19-	Signs for the Atkin-Lehner involutions
Class	38a	Isogeny class
Conductor	38	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	-152 = -1 · 23 · 19	Discriminant
Eigenvalues	2+  1  0 -1 -6  5  3 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-16,22]	[a1,a2,a3,a4,a6]
j	-413493625/152	j-invariant
L	0.6302107433141	L(r)(E,1)/r!
Ω	5.6718966898269	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	304b1 1216b1 342a1 950e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 38a3

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
+	1	0	-1	-6	5	3	-	3	9	-4	2	0	8	0	-3	9	-10	5	-6	-7	-10	-6	-12	-10

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Quadratic twists for elliptic curve 38a3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53
304b1	1216b1	342a1	950e1	1862b1	4598n1	6422f1	10982b1	722e1	20102b1	31958h1	36518a1	52022i1	63878c1	70262f1	83942a1	106742g1

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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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