Cremona's table of elliptic curves

4032 = 2⁶ · 3² · 7

Field	Data	Notes
Atkin-Lehner	2+ 3- 7-	Signs for the Atkin-Lehner involutions
Class	4032n	Isogeny class
Conductor	4032	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	-263473523712 = -1 · 210 · 37 · 76	Discriminant
Eigenvalues	2+ 3-  0 7- -6 -2  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4080,103304]	[a1,a2,a3,a4,a6]
Generators	[10:252:1]	Generators of the group modulo torsion
j	-10061824000/352947	j-invariant
L	3.5648217300693	L(r)(E,1)/r!
Ω	0.97566368032908	Real period
R	0.30447836021279	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	4032bb3 252a3 1344d3 100800ej3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4032n3

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

---

Quadratic twists for elliptic curve 4032n3

-4	8	-3	5	-7
4032bb3	252a3	1344d3	100800ej3	28224bo3

---

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