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	4	Product of Tamagawa factors cp
Δ	7311624327 = 310 · 73 · 192	Discriminant
Eigenvalues	1 3+  0 7+ -2 -4 -4 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1925,31458]	[a1,a2,a3,a4,a6]
Generators	[-34:260:1]	Generators of the group modulo torsion
j	789529529265625/7311624327	j-invariant
L	1.8881722279102	L(r)(E,1)/r!
Ω	1.3293482923248	Real period
R	1.4203743584821	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	6384be2 25536bg2 1197d2 9975p2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 399a2

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

---

Quadratic twists for elliptic curve 399a2

-4	8	-3	5	-7	-11	13	17	-19
6384be2	25536bg2	1197d2	9975p2	2793j2	48279j2	67431f2	115311r2	7581e2

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations