Cremona's table of elliptic curves

1008 = 2⁴ · 3² · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 7+	Signs for the Atkin-Lehner involutions
Class	1008i	Isogeny class
Conductor	1008	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-83607552 = -1 · 214 · 36 · 7	Discriminant
Eigenvalues	2- 3-  0 7+  0 -4 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-75,506]	[a1,a2,a3,a4,a6]
Generators	[5:16:1]	Generators of the group modulo torsion
j	-15625/28	j-invariant
L	2.4075899134388	L(r)(E,1)/r!
Ω	1.7158924675379	Real period
R	0.70155617528104	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	126a1 4032z1 112c1 25200eh1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1008i1

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

---

Quadratic twists for elliptic curve 1008i1

-4	8	-3	5	-7	-11
126a1	4032z1	112c1	25200eh1	7056bp1	121968fl1

---

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