Cremona's table of elliptic curves

4128 = 2⁵ · 3 · 43

Field	Data	Notes
Atkin-Lehner	2- 3- 43+	Signs for the Atkin-Lehner involutions
Class	4128n	Isogeny class
Conductor	4128	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-8520192 = -1 · 29 · 32 · 432	Discriminant
Eigenvalues	2- 3-  2 -2  0 -6  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-32,-168]	[a1,a2,a3,a4,a6]
Generators	[34:198:1]	Generators of the group modulo torsion
j	-7301384/16641	j-invariant
L	4.4945141957963	L(r)(E,1)/r!
Ω	0.93588955292062	Real period
R	2.4011990420079	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	4128b2 8256k2 12384f2 103200g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4128n2

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

---

Quadratic twists for elliptic curve 4128n2

-4	8	-3	5
4128b2	8256k2	12384f2	103200g2

---

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