Cremona's table of elliptic curves

3999 = 3 · 31 · 43

Field	Data	Notes
Atkin-Lehner	3- 31- 43+	Signs for the Atkin-Lehner involutions
Class	3999a	Isogeny class
Conductor	3999	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	-1115721 = -1 · 33 · 312 · 43	Discriminant
Eigenvalues	-1 3- -3 -1  3  1 -2 -5	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2,-51]	[a1,a2,a3,a4,a6]
Generators	[13:40:1]	Generators of the group modulo torsion
j	-912673/1115721	j-invariant
L	2.1987105385613	L(r)(E,1)/r!
Ω	1.2428453994408	Real period
R	0.29484902675085	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	63984s1 11997a1 99975d1 123969b1	Quadratic twists by: -4 -3 5 -31

Hecke Eigenvalues for elliptic curve 3999a1

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	-	-3	-1	3	1	-2	-5	0	-5	-	12	6	+	9	-6	4	-2	2	2	8	4	-9	10	-19

---

Quadratic twists for elliptic curve 3999a1

-4	-3	5	-31
63984s1	11997a1	99975d1	123969b1

---

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