Cremona's table of elliptic curves

5568 = 2⁶ · 3 · 29

Field	Data	Notes
Atkin-Lehner	2- 3+ 29-	Signs for the Atkin-Lehner involutions
Class	5568y	Isogeny class
Conductor	5568	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	2511212544 = 212 · 36 · 292	Discriminant
Eigenvalues	2- 3+ -2  0 -4  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1049,13209]	[a1,a2,a3,a4,a6]
Generators	[-8:145:1]	Generators of the group modulo torsion
j	31196377792/613089	j-invariant
L	2.7697087926472	L(r)(E,1)/r!
Ω	1.446562773935	Real period
R	1.9146827517985	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	5568bf2 2784c1 16704ck2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 5568y2

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

---

Quadratic twists for elliptic curve 5568y2

-4	8	-3
5568bf2	2784c1	16704ck2

---

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