Cremona's table of elliptic curves

5768 = 2³ · 7 · 103

Field	Data	Notes
Atkin-Lehner	2+ 7+ 103+	Signs for the Atkin-Lehner involutions
Class	5768a	Isogeny class
Conductor	5768	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	152090624 = 211 · 7 · 1032	Discriminant
Eigenvalues	2+ -2 -2 7+  0  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-264,1456]	[a1,a2,a3,a4,a6]
Generators	[11:2:1]	Generators of the group modulo torsion
j	997354514/74263	j-invariant
L	2.1394621096208	L(r)(E,1)/r!
Ω	1.7886087495122	Real period
R	2.3923198521804	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	11536d2 46144a2 51912n2 40376d2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 5768a2

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	2	2	-4	4	-6	-4	-4	-2	12	0	-4	12	14	8	2	4	-12	16	0	10

---

Quadratic twists for elliptic curve 5768a2

-4	8	-3	-7
11536d2	46144a2	51912n2	40376d2

---

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