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	2	Product of Tamagawa factors cp
deg	168	Modular degree for the optimal curve
Δ	1008273 = 3 · 72 · 193	Discriminant
Eigenvalues	-1 3-  4 7+ -2  4  0 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-431,3408]	[a1,a2,a3,a4,a6]
j	8855610342769/1008273	j-invariant
L	1.3331183260701	L(r)(E,1)/r!
Ω	2.6662366521403	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	6384z1 25536l1 1197c1 9975d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 399c1

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 399c1

-4	8	-3	5	-7	-11	13	17	-19
6384z1	25536l1	1197c1	9975d1	2793d1	48279bb1	67431t1	115311h1	7581c1

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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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