Cremona's table of elliptic curves

1666 = 2 · 7² · 17

Field	Data	Notes
Atkin-Lehner	2- 7- 17-	Signs for the Atkin-Lehner involutions
Class	1666m	Isogeny class
Conductor	1666	Conductor
∏ cp	56	Product of Tamagawa factors cp
Δ	10449324411008 = 27 · 710 · 172	Discriminant
Eigenvalues	2-  2  4 7- -6  2 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-34301,-2454509]	[a1,a2,a3,a4,a6]
j	37936442980801/88817792	j-invariant
L	4.9120403599749	L(r)(E,1)/r!
Ω	0.35086002571249	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	13328y2 53312bd2 14994ba2 41650o2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1666m2

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	-	-6	2	-	0	-4	8	0	4	2	-8	8	-6	4	8	-16	4	-10	-12	-12	-10	-6

---

Quadratic twists for elliptic curve 1666m2

-4	8	-3	5	-7	17
13328y2	53312bd2	14994ba2	41650o2	238a2	28322bb2

---

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