Cremona's table of elliptic curves

399 = 3 · 7 · 19

Field	Data	Notes
Atkin-Lehner	3- 7+ 19+	Signs for the Atkin-Lehner involutions
Class	399c	Isogeny class
Conductor	399	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	2963890503 = 32 · 7 · 196	Discriminant
Eigenvalues	-1 3-  4 7+ -2  4  0 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-466,2813]	[a1,a2,a3,a4,a6]
j	11192824869409/2963890503	j-invariant
L	1.3331183260701	L(r)(E,1)/r!
Ω	1.3331183260701	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6384z2 25536l2 1197c2 9975d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 399c2

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

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Quadratic twists for elliptic curve 399c2

-4	8	-3	5	-7	-11	13	17	-19
6384z2	25536l2	1197c2	9975d2	2793d2	48279bb2	67431t2	115311h2	7581c2

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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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