Cremona's table of elliptic curves

16428 = 2² · 3 · 37²

Field	Data	Notes
Atkin-Lehner	2- 3- 37+	Signs for the Atkin-Lehner involutions
Class	16428d	Isogeny class
Conductor	16428	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-8092752661833984 = -1 · 28 · 32 · 378	Discriminant
Eigenvalues	2- 3-  2 -4 -4  6 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,48828,1235700]	[a1,a2,a3,a4,a6]
Generators	[-308334:10749045:17576]	Generators of the group modulo torsion
j	19600688/12321	j-invariant
L	5.8663329011284	L(r)(E,1)/r!
Ω	0.25740261275431	Real period
R	11.395247387655	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	65712s2 49284k2 444b2	Quadratic twists by: -4 -3 37

Hecke Eigenvalues for elliptic curve 16428d2

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

---

Quadratic twists for elliptic curve 16428d2

-4	-3	37
65712s2	49284k2	444b2

---

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