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	646d	Isogeny class
Conductor	646	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	25137152 = 212 · 17 · 192	Discriminant
Eigenvalues	2-  0 -2 -2 -2 -6 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-406,3237]	[a1,a2,a3,a4,a6]
Generators	[9:11:1]	Generators of the group modulo torsion
j	7384117376817/25137152	j-invariant
L	2.5834562462254	L(r)(E,1)/r!
Ω	2.1316501108737	Real period
R	0.20199189296647	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	5168c1 20672a1 5814j1 16150j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 646d1

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

---

Quadratic twists for elliptic curve 646d1

-4	8	-3	5	-7	-11	13	17	-19
5168c1	20672a1	5814j1	16150j1	31654t1	78166c1	109174a1	10982f1	12274b1

---

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