Cremona's table of elliptic curves

666 = 2 · 3² · 37

Field	Data	Notes
Atkin-Lehner	2- 3- 37-	Signs for the Atkin-Lehner involutions
Class	666g	Isogeny class
Conductor	666	Conductor
∏ cp	46	Product of Tamagawa factors cp
deg	19872	Modular degree for the optimal curve
Δ	-4453592173903872 = -1 · 223 · 315 · 37	Discriminant
Eigenvalues	2- 3-  4  3 -5  3 -3 -7	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1640858,-808607271]	[a1,a2,a3,a4,a6]
j	-670206957616537490521/6109179936768	j-invariant
L	3.0680287440076	L(r)(E,1)/r!
Ω	0.066696277043644	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5328x1 21312q1 222e1 16650n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 666g1

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
-	-	4	3	-5	3	-3	-7	-9	0	-2	-	-6	4	10	-3	4	-2	6	12	13	-6	-5	-11	6

---

Quadratic twists for elliptic curve 666g1

-4	8	-3	5	-7	-11	13	37
5328x1	21312q1	222e1	16650n1	32634ci1	80586t1	112554e1	24642j1

---

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