Cremona's table of elliptic curves

646 = 2 · 17 · 19

Field	Data	Notes
Atkin-Lehner	2- 17+ 19+	Signs for the Atkin-Lehner involutions
Class	646c	Isogeny class
Conductor	646	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	448	Modular degree for the optimal curve
Δ	8861828 = 22 · 17 · 194	Discriminant
Eigenvalues	2- -2  4  4  2 -6 17+ 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-241,1413]	[a1,a2,a3,a4,a6]
j	1548415333009/8861828	j-invariant
L	2.3277953902704	L(r)(E,1)/r!
Ω	2.3277953902704	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	5168h1 20672k1 5814h1 16150e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 646c1

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	2	-6	+	+	0	-8	8	-4	10	0	-8	-6	0	-8	8	-12	-6	-4	8	18	2

---

Quadratic twists for elliptic curve 646c1

-4	8	-3	5	-7	-11	13	17	-19
5168h1	20672k1	5814h1	16150e1	31654w1	78166h1	109174e1	10982d1	12274e1

---

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