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	399a	Isogeny class
Conductor	399	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	120	Modular degree for the optimal curve
Δ	543185433 = 35 · 76 · 19	Discriminant
Eigenvalues	1 3+  0 7+ -2 -4 -4 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-210,-441]	[a1,a2,a3,a4,a6]
Generators	[-10:33:1]	Generators of the group modulo torsion
j	1031831907625/543185433	j-invariant
L	1.8881722279102	L(r)(E,1)/r!
Ω	1.3293482923248	Real period
R	2.8407487169643	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	6384be1 25536bg1 1197d1 9975p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 399a1

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	+	-2	-4	-4	+	2	-2	0	6	-6	8	0	-2	4	-10	14	-12	10	10	-12	-6	-4

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Quadratic twists for elliptic curve 399a1

-4	8	-3	5	-7	-11	13	17	-19
6384be1	25536bg1	1197d1	9975p1	2793j1	48279j1	67431f1	115311r1	7581e1

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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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