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	3	Product of Tamagawa factors cp
deg	6	Modular degree for the optimal curve
Δ	-3511808 = -1 · 29 · 193	Discriminant
Eigenvalues	2+  1  0 -1 -6  5  3 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,9,90]	[a1,a2,a3,a4,a6]
j	94196375/3511808	j-invariant
L	0.6302107433141	L(r)(E,1)/r!
Ω	1.8906322299423	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	304b2 1216b2 342a2 950e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 38a1

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 38a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53
304b2	1216b2	342a2	950e2	1862b2	4598n2	6422f2	10982b2	722e2	20102b2	31958h2	36518a2	52022i2	63878c2	70262f2	83942a2	106742g2

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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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