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	4032o	Isogeny class
Conductor	4032	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	9029615616 = 216 · 39 · 7	Discriminant
Eigenvalues	2+ 3-  2 7-  0 -6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-145164,-21288080]	[a1,a2,a3,a4,a6]
Generators	[4005:252265:1]	Generators of the group modulo torsion
j	7080974546692/189	j-invariant
L	4.0840139470947	L(r)(E,1)/r!
Ω	0.24458781858393	Real period
R	8.3487680840764	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	4032bd4 504g3 1344j4 100800db4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4032o3

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	-	0	-6	2	-4	4	-10	-8	-6	2	4	-8	-10	12	2	-12	12	-14	-8	12	2	10

---

Quadratic twists for elliptic curve 4032o3

-4	8	-3	5	-7
4032bd4	504g3	1344j4	100800db4	28224ce4

---

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