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	2	Product of Tamagawa factors cp
deg	416	Modular degree for the optimal curve
Δ	8256 = 26 · 3 · 43	Discriminant
Eigenvalues	2- 3-  2 -2  0 -6  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-42,-120]	[a1,a2,a3,a4,a6]
Generators	[255:550:27]	Generators of the group modulo torsion
j	131096512/129	j-invariant
L	4.4945141957963	L(r)(E,1)/r!
Ω	1.8717791058412	Real period
R	4.8023980840158	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	4128b1 8256k1 12384f1 103200g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4128n1

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 4128n1

-4	8	-3	5
4128b1	8256k1	12384f1	103200g1

---

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