Cremona's table of elliptic curves

4056 = 2³ · 3 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3- 13+	Signs for the Atkin-Lehner involutions
Class	4056f	Isogeny class
Conductor	4056	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	192763444224 = 210 · 3 · 137	Discriminant
Eigenvalues	2+ 3- -2  0  0 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-140664,-20352864]	[a1,a2,a3,a4,a6]
j	62275269892/39	j-invariant
L	1.972166420519	L(r)(E,1)/r!
Ω	0.24652080256488	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	8112b3 32448c4 12168n3 101400ca4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4056f3

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	0	+	2	4	0	6	0	2	-6	-12	4	6	8	-2	-4	12	14	0	-8	18	6

---

Quadratic twists for elliptic curve 4056f3

-4	8	-3	5	13
8112b3	32448c4	12168n3	101400ca4	312c3

---

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